Search

Let DN be the set of points around which a planar Brownian motion winds at least N times. We prove that the random measure on the plane with density 2πN1DN with respect to the Lebesgue measure converges almost surely weakly, as N tends to infinity, towards the occupation measure of the Brownian motion. [ABSTRACT FROM AUTHOR]

In this study, the mass densities from Challenging Minisatellite Payload and Gravity Recovery and Climate Experiment satellites and the simulation results from the Thermosphere Ionosphere Electrodynamics General Circulation Model (TIEGCM) have been used to systematically explore the peak response time (or time delay hereafter) of thermospheric mass density to the 27-day solar extreme ultraviolet (EUV) flux variation. The TIEGCM can generally reproduce the observed time delay of thermospheric mass density to the 27-day solar EUV flux changes. The simulation results suggest that the delay of the peak of thermospheric mass density to that of the 27-day solar EUV flux variation is about 0.9 days. However, geomagnetic activity can significantly affect the derivation of the time delay of thermospheric mass density from the pure solar EUV flux impact. Additionally, the delay of thermospheric mass density to the 27-day solar EUV flux changes with altitude, latitude, and local time. [ABSTRACT FROM AUTHOR]

This study analyzes the characteristics of non-substorm Pi2 (impulsive pulsations [3-25 mHz]) from low and middle latitudes and investigates the trends of these oscillations. Pi2 events are identified from geomagnetic H-component data from low and middle latitude observatories Hyderabad (HYB, L 1.03) and Paratunka (PET, L 2.1) respectively, during solar maximum period (2015-2016) for quietest geomagnetic conditions, with stringent criteria of interplanetary parameters and activity indices. Data from five high-latitude stations from THEMIS ground magnetometer chain, covering all local time sectors are additionally analyzed to verify the absence of substorms, pseudo substorms, etc. which may also generate Pi2 signatures. Variation of non-substorm Pi2 periods with geomagnetic activity index Kp and solar wind speed (Vsw) show inverse relations with Pi2 period at HYB. In addition, non-substorm Pi2s are distributed equally in all local time sectors with ratio of second harmonic to fundamental Pi2 ranging within 1.3-2.2. These trends of non-substorm Pi2s indicate plasmaspheric cavity resonance (PCR) as the dominant source at low latitude, confirmed using a theoretical model. In contrast, non-substorm Pi2 periods do not show a steady trend with Kp and Vsw at midlatitude station PET. Local time variations show an increased period in the premidnight sector at PET. A close agreement between theoretical estimates and observed periods of non-substorm Pi2-s at PET, leads to the inference of Alfvenic nature of these modes, attributable to a resonant oscillation. [ABSTRACT FROM AUTHOR]

This education article presents a case for first courses on Markov chain modeling to include the topic "sojourn time cycle chart"" (STC chart). This article does so through a teaching module that consists of (i) hypothetical examples illustrating the application-motivated concept of STC chart, and (ii) a network-based procedure for computing sojourn times of finite Markov chains inside subsets of their states. The sojourn time computation procedure is a simplified version of computations that already exist in several journal articles, and it applies to discrete-time Markov chain (DTMC), continuous-time Markov chain (CTMC) in rate form, and CTMC in time form. The only requirement for success in the computations is that Markov chain balance equations have a unique solution. [ABSTRACT FROM AUTHOR]

We study the asymptotic behavior of the mean sojourn time for a random walk above a receding curved boundary in the case where the jump distribution satisfies the Cramèr condition. [ABSTRACT FROM AUTHOR]

This paper presents a simple algorithm for computing the cumulative distribution function of the sojourn time of a random customer in an M/GL/1 queue with bulk-service of exactly size L. Both theoretical and numerical aspects related to this problem were not discussed by Chaudhry and Templeton in their monograph (1983). Our analysis is based on the roots of the so-called characteristic equation of the Laplace-Stieltjes transform (LST) of the sojourn time distribution. Using the method of partial fractions and residue theorem, we obtain a closed-form expression of sojourn time distribution, from which we can calculate the value of the distribution function for any given time t ∈ [0, + ∞). Finally, to ensure the reliability of the analytical procedure, employing the work done by Gross and Harris (1985), an effective way to validate the correctness of our results along with some numerical examples are also provided. [ABSTRACT FROM AUTHOR]

A time-local Fokker–Planck equation (TLFPE) is derived which accounts for memory effects in stochastic problems. This is expected to provide a computationally efficient method of modeling the phase space evolution of such systems by simple (local time) Langevin equations with Markovian fluctuating forces that are characterized by time-dependent moments; it is this explicit time dependence that describes the memory effects. The TLFPE is derived from the probability theory of non-Markovian systems as a generalization of Chandrasekar’s derivation of the Fokker–Planck equation (FPE) from the Chapman–Kolmogarov equation for Markovian systems. In this article it is applied to free particle diffusion and barrier crossing problems, and is shown to give rise to physically realistic results. Further, the form of the TLFPE suggests that the conditions required for systems to exhibit Markovian behavior are less restrictive than the Brownian criterion of separation of time scales between the fluctuating forces and the momentum response of the system. Rather, a sufficient condition is that the time-dependent moments of the TLFPE reach plateau values before the time scale of the phenomenon of interest. [ABSTRACT FROM AUTHOR]

Biological evidence suggests that local time-frequency (LTF) information can be utilized to improve the recognition rate of sounds in the presence of noise. However, most of conventional methods use stationary (frequency-based) features which are not robust to noise, as each stationary feature contains a mixture of spectral information from both noise and signal. This paper proposes a spike-timing based model to encode and learn the LTF features extracted from sound spectrogram using spiking neural networks (SNNs), named LTF-SNN. In this model, we encode the reliable LTF features into spike train patterns and train with different spike-based learning rules. We analyze the efficacy of the spike-based feature encoding method and the recognition performance of the model by using two classes of SNN learning algorithms: ReSuMe and Tempotron. Utilizing the temporal coding and learning, networks of spiking neurons can effectively perform robust sound recognition tasks. Experimental results demonstrate that the model achieves superior performance in mismatched conditions compared with benchmark approaches. [ABSTRACT FROM AUTHOR]

We study American swaptions in the linear-rational (LR) term structure model introduced in Filipović et al. [J. Finance., 2017, 72, 655-704]. The American swaption pricing problem boils down to an optimal stopping problem that is analytically tractable. It reduces to a free-boundary problem that we tackle by the local time-space calculus of Peskir [J. Theoret. Probab., 2005a, 18, 499-535]. We characterize the optimal stopping boundary as the unique solution to a non-linear integral equation that can be readily solved numerically. We obtain the arbitrage-free price of the American swaption and the optimal exercise strategies in terms of swap rates for both fixed-rate payer and receiver swaps. Finally, we show that Bermudan swaptions can be efficiently priced as well. [ABSTRACT FROM AUTHOR]

Abstract Let X be a regular one-dimensional transient diffusion and L y be its local time at y. The stochastic differential equation (SDE) whose solution corresponds to the process X conditioned on [ L ∞ y = a ] for a given a ≥ 0 is constructed and a new path decomposition result for transient diffusions is given. In the course of the construction Bessel-type motions as well as their SDE representations are studied. Moreover, the Engelbert–Schmidt theory for the weak solutions of one dimensional SDEs is extended to the case when the initial condition is an entrance boundary for the diffusion. This extension was necessary for the construction of the Bessel-type motion which played an essential part in the SDE representation of X conditioned on [ L ∞ y = a ]. [ABSTRACT FROM AUTHOR]

Abstract In this paper we consider the field of local times of a discrete-time Markov chain on a general state space, and obtain uniform (in time) upper bounds on the total variation distance between this field and the one of a sequence of n i.i.d. random variables with law given by the invariant measure of that Markov chain. The proof of this result uses a refinement of the soft local time method of Popov and Teixeira (2015). [ABSTRACT FROM AUTHOR]

We further investigate properties of the Gaussian free field (GFF) on the metric graph associated to a discrete weighted graph (where the edges of the latter are replaced by continuous line-segments of appropriate length) that has been introduced by the first author. On such a metric graph, the GFF is a random continuous function that generalises one-dimensional Brownian bridges so that one-dimensional techniques can be used. In the present paper, we define and study the pseudo-metric defined on the metric graph (and therefore also on the discrete graph itself), where the length of a path on the metric graph is defined to be the local time at level zero accumulated by the Gaussian free field along this path. We first derive a pathwise transformation that relates the GFF on the metric graph with the reflected GFF on the metric graph via the pseudo-distance defined by the latter. This is a generalisation of Paul Lévy’s result relating the local time at zero of Brownian motion to the supremum of another Brownian motion. We also compute explicitly the distribution of certain functionals of this pseudo-metric and of the GFF. In particular, we point out that when the boundary consists of just two points, the law of the pseudo-distance between them depends solely on the resistance of the network between them. We then discuss questions related to the scaling limit of this pseudo-metric in the two-dimensional case, which should be the conformally invariant way to measure distances between CLE(4) loops introduced and studied by the second author with Wu, and by Sheffield, Watson and Wu. Our explicit laws on metric graphs also lead to new conjectures for related functionals of the continuum GFF on fairly general Riemann surfaces. [ABSTRACT FROM AUTHOR]

We base ourselves on the construction of the two-dimensional random interlacements (Comets et al., 2016) to define the one-dimensional version of the process. For this, we consider simple random walks conditioned on never hitting the origin. We compare this process to the conditional random walk on the ring graph. Our results are the convergence of the vacant set on the ring graph to the vacant set of one-dimensional random interlacements, a central limit theorem for the interlacements’ local time and the convergence in law of the local times of the conditional walk on the ring graph to the interlacements’ local times. [ABSTRACT FROM AUTHOR]

In this paper we study time inhomogeneous versions of one-dimensional Stochastic Differential Equations (SDE) involving the Local Time of the unknown process on curves. After proving existence and uniqueness for these SDEs under mild assumptions, we explore their link with Parabolic Differential Equations (PDE) with transmission conditions. We study the regularity of solutions of such PDEs and ensure the validity of a Feynman–Kac representation formula. These results are then used to characterize the solutions of these SDEs as time inhomogeneous Markov Feller processes. [ABSTRACT FROM AUTHOR]

The functional Itô formula, firstly introduced by Bruno Dupire for continuous semimartingales, might be extended in two directions: different dynamics for the underlying process and/or weaker assumptions on the regularity of the functional. In this paper, we pursue the former type by proving the functional version of the Meyer–Tanaka formula. Following the idea of the proof of the classical time-dependent Meyer–Tanaka formula, we study the mollification of functionals and its convergence properties. As an example, we study the running maximum and the max-martingales of Yor and Obłój. [ABSTRACT FROM AUTHOR]

For the Processor Sharing queue with batch job arrivals, the sojourn time W of a single job is investigated. This queuing model is motivated by the evaluation of Cloud Computing or Virtualized Network systems where the treatment of micro-services within requests determines the global system performance. We first show that the distribution of sojourn time W can be obtained from an infinite linear differential system; the structure of this system, however, makes the explicit derivation of this distribution generally difficult. When further assuming that the batch size has a geometric distribution with some given parameter , this differential system can be analyzed via a single generating function which is shown to verify a second-order partial differential equation involving a boundary term at point . Solving this partial differential equation for with required analyticity properties determines the one-sided Laplace transform for given u. Writing in terms of a multivariate hypergeometric function enables one to extend its analyticity domain to a cut-plane , for negative constants and . By means of a Laplace inversion of for a suitable value of u, the complementary distribution function is then given an explicit integral representation. This enables us to show that the tail of this distribution has an exponential decay with rate , together with a sub-exponential factor. A convergence in distribution is also asserted for W in heavy load condition, the limit distribution exhibiting a sub-exponential behavior itself. Using our exact results for the sojourn time of a single job, we finally discuss an approximation for the distribution of the sojourn time of an entire batch when assuming that the batch size is not too large. [ABSTRACT FROM AUTHOR]

The empirical model of the location of the main ionospheric trough (MIT) is developed based on an analysis of data from CHAMP satellite measured at the altitudes of ~350-450 km during 2000-2007; the model is presented in the form of the analytical dependence of the invariant latitude of the trough minimum Φm on the magnetic local time (MLT), the geomagnetic activity, and the geographical longitude for the Northern and Southern Hemispheres. The time-weighted average index Kp(τ), the coefficient of which τ = 0.6 is determined by the requirement of the model minimum deviation from experimental data, is used as an indicator of geomagnetic activity. The model has no limitations, either in local time or geomagnetic activity. However, the initial set of MIT minima mainly contains data dealing with an interval of 16-08 MLT for Kp(τ) < 6; therefore, the model is rather qualitative outside this interval. It is also established that (a) the use of solar local time (SLT) instead of MLT increases the model error no more than by 5-10%; (b) the amplitude of the longitudinal effect at the latitude of MIT minimum in geomagnetic (invariant) coordinates is ten times lower than that in geographical coordinates. [ABSTRACT FROM AUTHOR]

We show that under some slight assumptions, the positive sojourn time of a product of symmetric processes converges towards 1/2 as the number of processes increases. Monotony properties are then exhibited in the case of symmetric stable processes, and used, via a recurrence relation, to obtain upper and lower bounds on the moments of the occupation time (in the first and third quadrants) for two-dimensional Brownian motion. Explicit values are also given for the second and third moments in the n-dimensional Brownian case. [ABSTRACT FROM AUTHOR]

In this paper we consider a discrete-time retrial queueing system with batch arrivals of geometric type and general batch services. The arriving group of customers can decide to go directly to the server expelling out of the system the batch of customers that is currently being served, if any, or to join the orbit. After a successful retrial all the customers in the orbit get service simultaneously. An extensive analysis of the model is carried out, and using a generating functions approach some performance measures of the model, such as the first distribution’s moments of the number of customers in the orbit and in the system, are obtained. The generating functions of the sojourn time of a customer in the orbit and in the system are also given. Finally, in the section of conclusions and research results the main contributions of the paper are commented. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish sharp estimates for the moduli of continuity of the local time of a class of sub-fractional Brownian motions. We also investigate the continuity of their local times with respect to the self-similarity index. [ABSTRACT FROM AUTHOR]

An application of semi-Markov models to AIDS disease progression was utilized to find best sojourn time distributions. We obtained data on 370 HIV/AIDS patients who were under follow-up from September 2008 to August 2015, from Yirgalim General Hospital, Ethiopia. The study reveals that within the "good" states, the transition probability of moving from a given state to the next worst state has a parabolic pattern that increases with time until it reaches a maximum and then declines over time. Compared with the case of exponential distribution, the conditional probability of remaining in a good state before moving to the next good state grows faster at the beginning, peaks, and then declines faster for a long period. The probability of remaining in the same good disease state declines over time, though maintaining higher values for healthier states. Moreover, the Weibull distribution under the semi-Markov model leads to dynamic probabilities with a higher rate of decline and smaller deviations. In this study, we found that the Weibull distribution is flexible in modeling and preferable for use as a waiting time distribution for monitoring HIV/AIDS disease progression. [ABSTRACT FROM AUTHOR]

On the basis of the passivity theory, the problem of designing non-fragile [ABSTRACT FROM AUTHOR]

LetX= {X(t)}t ⩾ 0be an operator semistable Lévy process onwith exponentE, whereEis an invertible linear operator on. In this article, we determine exact Hausdorff measure functions for the range ofXover the time interval [0, 1] under certain assumptions on the principal spectral component ofE. As a byproduct, we also present Tauberian results for semistable subordinators and sharp bounds for the asymptotic behavior of the expected sojourn times ofX. [ABSTRACT FROM AUTHOR]

In this paper, we study the basic properties of last-in first-out (LIFO) preemptive-repeat single-server queues in which the server needs to start service from scratch whenever a preempted customer reaches the server. In particular, we study the question of when such queues are stable (in the sense that the equilibrium time-in-system is finite-valued with probability one) and show how moments of the equilibrium customer sojourn time can be computed when the system is stable. A complete analysis of stability is provided in the setting of Poisson arrivals and in that of the Markovian arrival process. The stability region depends upon the detailed structure of the interarrival and service time distributions and cannot be expressed purely in terms of expected values. This is connected to the fact that such preemptive-repeat queues are not work conserving. [ABSTRACT FROM AUTHOR]

We consider an exponential queueing network that differs from a Gelenbe network (with the usual positive and so-called negative customers), first, in that the sojourn time of customers at the network nodes is bounded by a random value whose conditional distribution for a fixed number of customers in a node is exponential. Second, we significantly relax the conditions on possible values of parameters for incoming Poisson flows of positive and negative customers in Gelenbe's theorem. Claims serviced at the nodes and customers leaving the nodes at the end of their sojourn time can stay positive, become negative, or leave the network according to different routing matrices. We prove a theorem that generalizes Gelenbe's theorem. [ABSTRACT FROM AUTHOR]

There are significant differences (in the order of 3 to 20 K) between the lunar brightness temperatures (TBs) as measured by the microwave radiometers (MRM) onboard Chang'E (CE)−1 and −2. To determine which set is more accurate, we have carried out a dataset comparison using theoretical calculations of the TBs (four frequency channels) versus local time at the Apollo 15 and 17 landing sites, where the thermal parameters are well-constrained by the in-situ measurements. Based on these parameters, we sought to constrain fits between theory and observation, as uncertainties still exist in parameters involved in the microwave transfer computation. We found that: (i) CE-1/2 TBs have almost constant biases (negative, different for different channels) from the theoretical TBs. The averaged biases for each channel are smaller for CE-1; (ii) TBs of the high frequency channels (19.35/37 GHz) show a better fit with theory than the low frequency channels. The channel 4 (37 GHz) TBs from CE-1 are consistently shifted by about 1 K from the theoretical values. Adjustments in the order of 20 K are instead needed for the two CE-2 low frequency channels (3/7.8 GHz). Based on this comparison, we conclude that the CE-1 dataset to be more accurate than CE-2 one in terms of temperature accuracy (not spatial resolution). We also offer a possible explanation for the significant TB differences between CE-1 and CE-2, and propose a possible recalibration method as a starting point towards the realignment of the two datasets. [ABSTRACT FROM AUTHOR]

In this paper, a discontinuous Galerkin time-domain (DGTD) method is developed to analyze the power-ground planes taking into account the decoupling capacitors. In the presence of decoupling capacitors, the whole physical system can be split into two subsystems: 1) the field subsystem that is governed by Maxwell’s equations that will be solved by the DGTD method, and 2) the circuit subsystem including the capacitor and its parasitic inductor and resistor, which is going to be characterized by the modified nodal analysis algorithm constructed circuit equations. With the aim to couple the two subsystems together, a lumped port is defined over a coaxial surface between the via barrel and the ground plane. To reach the coupling from the field to the circuit subsystem, a lumped voltage source calculated by the integration of electric field along the radial direction is introduced. On the other hand, to facilitate the coupling from the circuit to field subsystem, a lumped port current source calculated from the circuit equation is introduced, which serves as an impressed current source for the field subsystem. With these two auxiliary terms, a hybrid field-circuit matrix equation is established, which enables the field and circuit subsystems are solved in a synchronous scheme. Furthermore, the arbitrarily shaped antipads are considered by enforcing the proper wave port excitation using the magnetic surface current source derived from the antipads supported electric eigenmodes. In this way, the S-parameters corresponding to different modes can be conveniently extracted. To further improve the efficiency of the proposed algorithm in handling multiscale meshes, the local time-stepping marching scheme is applied. The proposed algorithm is verified by several representative examples. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate an M/M/1 queue with a two-stage vacation policy which comprises of single working vacation and single vacation. Using the matrix-analytic method, we obtain the distribution of stationary system size, and then the decomposition structures of the stationary system size and the sojourn time are demonstrated. Furthermore, we study the waiting time by first-passage time analysis. Meanwhile, the busy-cycle analysis is provided by the limiting theorem of alternative renewal process. Finally, several numerical examples are presented in the paper. [ABSTRACT FROM PUBLISHER]

As part of a multi-study project, this test-retest study seeks to identify the relations between studying abroad and a sojourner's personality as measured by the Big Five personality traits. It thereby attempts to answer the questions of who chooses to study abroad and how study abroad changes personality. A total of 221 students from a German university were tracked over the course of a semester, with the Big Five being obtained via a German version of the Big Five Inventory (Lang, Lüdtke, & Asendorpf, 2001) both at the beginning and at the end. The share of 93 students who studied abroad were found to rate higher in agreeableness and openness prior to the international experience than their fellow students who did not sojourn. In turn, sojourning evoked increases in both extraversion and agreeableness and a decrease in neuroticism. Upon inclusion of interaction terms of initial Big Five levels and study abroad status, positive main effects of study abroad and negative interaction effects for both agreeableness and conscientiousness could be observed. [ABSTRACT FROM AUTHOR]

We prove that the local time process of a planar simple random walk, when time is scaled logarithmically, converges to a non-degenerate pure jump process. The convergence takes place in the Skorokhod space with respect to the M1 topology and fails to hold in the J1 topology. [ABSTRACT FROM AUTHOR]

The presence of very few statistical studies on auroral omega bands motivated us to test-use a semi-automatic method for identifying large-scale undulations of the diffuse aurora boundary and to investigate their occurrence. Five identical all-sky cameras with overlapping fields of view provided data for 438 auroral omega-like structures over Fennoscandian Lapland from 1996 to 2007. The results from this set of omega band events agree remarkably well with previous observations of omega band occurrence in magnetic local time (MLT), lifetime, location between the region 1 and 2 field-aligned currents, as well as current density estimates. The average peak emission height of omega forms corresponds to the estimated precipitation energies of a few keV, which experienced no significant change during the events. Analysis of both local and global magnetic indices demonstrates that omega bands are observed during substorm expansion and recovery phases that are more intense than average substorm expansion and recovery phases in the same region. The omega occurrence with respect to the substorm expansion and recovery phases is in a very good agreement with an earlier observed distribution of fast earthward flows in the plasma sheet during expansion and recovery phases. These findings support the theory that omegas are produced by fast earthward flows and auroral streamers, despite the rarity of good conjugate observations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the stochastic heat equation of the form where $\frac{\partial^{2}B}{\partial t\,\partial x}$ is a fractional Brownian sheet with Hurst indices $H_{1},H_{2}\in(\frac{1}{2},1)$ and $\Delta _{\alpha}=-(-\Delta)^{\alpha/2}$ is a fractional Laplacian operator with $1<\alpha\leq2$ . In particular, when $H_{2}=\frac{1}{2}$ we show that the temporal process $\{u(t,\cdot),0\leq t\leq T\}$ admits a nontrivial p-variation with $p=\frac{2\alpha}{2\alpha H_{1}-1}$ and study its local nondeterminism and existence of the local time. [ABSTRACT FROM AUTHOR]

In multi-scale complex media, finite element meshes often require areas of local refinement, creating small elements that can dramatically reduce the global time-step for wave-propagation problems due to the CFL condition. Local time stepping (LTS) algorithms allow an explicit time-stepping scheme to adapt the time-step to the element size, allowing near-optimal time-steps everywhere in the mesh. We develop an efficient multilevel LTS-Newmark scheme and implement it in a widely used continuous finite element seismic wave-propagation package. In particular, we extend the standard LTS formulation with adaptations to continuous finite element methods that can be implemented very efficiently with very strong element-size contrasts (more than 100x). Capable of running on large CPU and GPU clusters, we present both synthetic validation examples and large scale, realistic application examples to demonstrate the performance and applicability of the method and implementation on thousands of CPU cores and hundreds of GPUs. [ABSTRACT FROM AUTHOR]

In the present paper, the perception of the seasonal variation of the Sq focus position is re-examined during low solar activity period (2006–2010). Equivalent current vectors are plotted for each geomagnetic quiet day (Ap ⩽ 5), using diurnal variations of H and D components measured at the magnetic observatories located in a narrow longitudinal belt of the Indo-Russian region. On the formation of well-defined Sq current loop, the information about the Sq focus is extracted by identifying a pair of neighboring stations with opposite zonal currents and nearby local times with opposite meridional currents. Thus, the method employed here is different from the methods used in earlier studies. Prominent seasonal variations in the Sq focus latitude, as well as in the local time of Sq focus, are observed. It is observed that the Sq focus is located at ∼30 deg in March equinox, but it moves to lower latitudes in the month of September. In winter, it shows large variability and also the formation of clear Sq current loop is less frequent. The local time of Sq focus is at ∼12 LT in March and shifts to ∼10 LT during September. It is clearly evident from the present analysis that the March and September equinoxes behave differently. The dominance of DE3 and semidiurnal waves in the September equinox could be the reason for the observed disparity. [ABSTRACT FROM AUTHOR]

We consider one-dimensional stochastic equations involving local times of unknown processes. We interpret these equations as diffusion in layered media with semi-permeable barriers and we study the limit behavior of solutions as barriers compress in one barrier. Conditions for convergence in law and limit equation are obtained. [ABSTRACT FROM AUTHOR]

To clarify the effect of the dawn and dusk terminators on Pi2 pulsations, we statistically analyzed the longitudinal phase and amplitude structures of Pi2 pulsations at middle- to low-latitude stations (GMLat = 5.30°-46.18°) around both the dawn and dusk terminators. Although the H (north-south) component Pi2s were affected by neither the local time (LT) nor the terminator location (at 100 km altitude in the highly conducting E region), some features of the D (east-west) component Pi2s depended on the location of the terminator rather than the LT. The phase reversal of the D component occurred 0.5-1 h after sunrise and 1-2 h before sunset. These phase reversals can be attributed to a change in the contributing currents from field-aligned currents (FACs) on the nightside to the meridional ionospheric currents on the sunlit side of the terminator, and vice versa. The phase reversal of the dawn terminator was more frequent than that of the dusk terminator. The D-to- H amplitude ratio on the dawn side began to increase at sunrise, reaching a peak approximately 2 h after sunrise (the sunward side of the phase reversal region), whereas the ratio on the dusk side reached a peak at sunset (the antisunward side). The dawn-dusk asymmetric features suggest that the magnetic contribution of the nightside FAC relative to the meridional ionospheric current on the dusk side is stronger than that on the dawn side, indicating that the center of Pi2-associated FACs, which probably corresponds to the Pi2 energy source, tends to be shifted duskward on average. Different features and weak sunrise/sunset dependences at the middle-latitude station (Paratunka, GMLat = 46.18°) can be attributed to the larger annual variation in the sunrise/sunset time and a stronger magnetic effect because of closeness from FACs. The D-to- H amplitude ratio decreased with decreasing latitude, suggesting that the azimuthal magnetic field produced by the FACs in darkness and the meridional ionospheric current in sunlight also decreased with decreasing latitude. [ABSTRACT FROM AUTHOR]

We provide a short proof of the Ray-Knight second generalized Theorem, using a martingale which can be seen (on the positive quadrant) as the Radon-Nikodym derivative of the reversed vertex-reinforced jump process measure with respect to the Markov jump process with the same conductances. Next we show that a variant of this process provides an inversion of that Ray-Knight identity. We give a similar result for the Ray-Knight first generalized Theorem. [ABSTRACT FROM AUTHOR]

The present survey is devoted to the investigation of the local times of self-intersection as the most important geometric characteristics of random processes. The trajectories of random processes are, as a rule, very nonsmooth curves. This is why to characterize the geometric shape of the trajectory it is impossible to use the methods of differential geometry. Instead of this, one can consider the local times of self-intersection showing how much time the process stays in 'small' vicinities of its points of self-intersection. We try to describe the current state of the theory of local times of self-intersection for Gaussian and related random processes. Different approaches to the definition, investigation, and application of the local times of self-intersection are considered. [ABSTRACT FROM AUTHOR]

For a Zd-valued random walk (Sn)n∈N0, let l(n,x) be its local time at the site x∈Zd. For α∈N, define the α-fold self-intersection local time as Ln(α)≔∑xl(n,x)α. Also let LnSRW(α) be the corresponding quantities for the simple random walk in Zd. Without imposing any moment conditions, we show that the variance of the self-intersection local time of any genuinely d-dimensional random walk is bounded above by the corresponding quantity for the simple symmetric random walk; that is, var(Ln(α))=O(var⁡(LnSRW(α))). In particular, for any genuinely d-dimensional random walk, with d≥4, we have var⁡(Ln(α))=O(n). On the other hand, in dimensions d≤3 we show that if the behaviour resembles that of simple random walk, in the sense that lim infn→∞var⁡Lnα/var⁡(LnSRW(α))>0, then the increments of the random walk must have zero mean and finite second moment. [ABSTRACT FROM AUTHOR]

We consider a single server renewal input queueing system under multiple vacation policy. When the system becomes empty, the server commences a vacation of random length, and either begins an ordinary vacation with probability q (0 ≤ q ≤ 1) or takes a working vacation with probability 1 - q. During a working vacation period, customers can be served at a rate lower than the service rate during a normal busy period. If there are cus- tomers in the system at a service completion instant, the working vacation can be interrupted and the server will come back to a normal busy period with probability p (0 ≤ q ≤ 1) or continue the working vacation with probability 1 - p. The server leaves for repeated vacations as soon as the system becomes empty. Upon arrival, customers decide for themselves whether to join or to balk, based on the observation of the system-length and/or state of the server. The equilibrium threshold balking strategies of customers under four cases: fully observable, almost observable, almost unobservable and fully unobservable have been studied using embedded Markov chain approach and linear reward-cost structure. The probability distribution of the system-length at pre-arrival epoch is derived using the roots method and then the system-length at an arbitrary epoch is derived with the help of the Markov renewal theory and semi-Markov processes. Various performance measures such as mean system-length, sojourn times, net benefit are derived. Finally, we present several numerical results to demonstrate the effect of the system parameters on the performance measures. [ABSTRACT FROM AUTHOR]

In Sigman (J. Appl. Probab. 48A:209-216, ), a first exact simulation algorithm was presented for the stationary distribution of customer delay for FIFO M/ G/ c queues in which ρ= λ/ μ<1 (super stable case). The key idea involves dominated coupling from the past while using the M/ G/1 queue under the processor sharing (PS) discipline as a sample-path upper bound, taking advantage of its time-reversibility properties so as to be able to simulate it backwards in time. Here, we expand upon this method and give several examples of other queueing models for which this method can be used to exactly simulate from their stationary distributions. Examples include sojourn times for single-server queues under various service disciplines, tandem queues, and multi-class networks with general routing. [ABSTRACT FROM AUTHOR]

RapidScat, which is a Ku-band scatterometer mounted on the International Space Station, observes the Earth's surface in a non-sun-synchronous orbit allowing for different local time-of-day (LTOD) observations as the orbit progresses. The unique orbit and different LTOD observations provide surface observations that are composited to describe the diurnal variability of Ku-band normalized backscatter (\sigma^0) measurements over land globally. Previous sun-synchronous scatterometers providing twice-daily surface observations have been used to demonstrate some diurnal changes in \sigma^0 in several regions globally, but instrument cross-calibration concerns prevent identifying diurnal changes by combining \sigma^0 observations from multiple sensors. As a result, the full extent of diurnal changes to \sigma^0 has not been determined until now. In this paper, RapidScat is used to identify diurnal changes to \sigma^0 globally. Vegetation type is discussed with respect to the diurnal changes in \sigma^0 regionally. The global diurnal changes to \sigma^0 are discussed with emphasis on the Amazon, Congo, and Upper Danube river regions. Diurnal cycles are described that could not previously be identified with sun-synchronous instruments. Global means and the magnitude of the diurnal cycle are discussed. With the diurnal changes identified and quantified, RapidScat can be used for future cross-platform calibrations using land targets. [ABSTRACT FROM AUTHOR]

Recently we pointed out the so-called local time scheme as a novel approach to quantum foundations that solves the preferred pointer-basis problem. In this paper, we introduce and analyse in depth a rather non-standard dynamical map that is imposed by the scheme. On the one hand, the map does not allow for introducing a properly defined generator of the evolution nor does it represent a quantum channel. On the other hand, the map is linear, positive, trace preserving and unital as well as completely positive, but is not divisible and therefore non- Markovian. Nevertheless, we provide quantitative criteria for dynamical emergence of time-coarsegrained Markovianity, for exact dynamics of an open system, as well as for operationally defined approximation of a closed or open many-particle system. A closed system never reaches a steady state, whereas an open system may reach a unique steady state given by the Lüders-von Neumann formula; where the smaller the open system, the faster a steady state is attained. These generic findings extend the standard open quantum systems theory and substantially tackle certain cosmological issues. [ABSTRACT FROM AUTHOR]