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Abstract Matsubara–Usuba [13] introduced the notion of skinniness and its variants for subsets of P κ λ and showed that the existence of skinny stationary subsets of P κ λ is related to large cardinal properties of ideals over P κ λ and to Jensen's diamond principle on λ. In this paper, we study the existence of skinny stationary sets in more detail. [ABSTRACT FROM AUTHOR]

Abstract We develop a forcing poset with finite conditions which adds a partial square sequence on a given stationary set, with adequate sets of models as side conditions. We then develop a kind of side condition product forcing for simultaneously adding partial square sequences on multiple stationary sets. We show that certain quotients of such forcings have the ω 1 -approximation property. We apply these ideas to prove, assuming the consistency of a greatly Mahlo cardinal, that it is consistent that the approachability ideal I [ ω 2 ] does not have a maximal set modulo clubs. [ABSTRACT FROM AUTHOR]

Abstract Regular pattern is a typical feature of vegetation distribution which can be recognized as early warnings of desertification. In this work, a vegetation system with cross diffusion is presented based on reaction-diffusion equations. By means of mathematical analysis, we obtain the appropriate parameter space which can ensure the emergence of stationary patterns. Moreover, it is unveiled that cross diffusion not only induces the pattern transitions, yet promotes the density of the vegetation. These obtained results suggest that cross diffusion is an important mechanism in vegetation dynamics. [ABSTRACT FROM AUTHOR]

A deep analysis of the Lyapunov exponents for stationary sequence of matrices going back to Furstenberg, for more general linear cocycles by Ledrappier, and generalized to the context of non-linear cocycles by Avila and Viana, gives an invariance principle for invariant measures with vanishing central exponents. In this paper, we give a new criterium formulated in terms of entropy for the invariance principle and, in particular, obtain a simpler proof for some of the known invariance principle results. As a byproduct, we study ergodic measures of partially hyperbolic diffeomorphisms whose center foliation is one-dimensional and forms a circle bundle. We show that for any such C² diffeomorphism which is accessible, weak hyperbolicity of ergodic measures of high entropy implies that the system itself is of rotation type. [ABSTRACT FROM AUTHOR]

Some general conditions for multichannel sampling are established for wide sense stationary sequences with spectral density. First, necessary and sufficient conditions are given for these processes so that they are linearly determined by the samples obtained from a multichannel sampling scheme. Some results are studied for stationary sequences and then applied to the problem of sampling, not necessarily band limited, wide sense stationary processes. Conditions are also given for the existence of a frame sequence of the samples. In the case of frames, the condition that the spectral measure is absolutely continuous is proved to be necessary. [ABSTRACT FROM AUTHOR]

The thermodynamic and stochastic theory of chemical systems far from equilibrium is extended to reactions in inhomogeneous system for both single and multiple intermediates, with multiple stationary states coupled with linear diffusion. The theory is applied to the two variable Selkov model coupled with diffusion, in particular to the issue of relative stability of two stable homogeneous stationary states as tested in a possible inhomogeneous experimental configuration. The thermodynamic theory predicts equistability of such states when the excess work from one stationary state to the stable inhomogeneous concentration profile equals the excess work from the other stable stationary state. The predictions of the theory on the conditions for relative stability are consistent with solutions of the deterministic reaction-diffusion equations. In the following article we apply the theory again to the issue of relative stability for single-variable systems, and make comparison with numerical solutions of the reaction-diffusion equations for the Schlögl model, and with experiments on an optically bistable system where the kinetic variable is temperature and the transport mechanism is thermal conduction. [ABSTRACT FROM AUTHOR]

The extremal index is an important parameter in the characterization of extreme values of a stationary sequence. Our new estimation approach for this parameter is based on the extremal behavior under the local dependence condition D(k)(un). We compare a process satisfying one of this hierarchy of increasingly weaker local mixing conditions with a process of cycles satisfying the D(2)(un) condition. We also analyze local dependence within moving maxima processes and derive a necessary and sufficient condition for D(k)(un). In order to evaluate the performance of the proposed estimators, we apply an empirical diagnostic for local dependence conditions, we conduct a simulation study and compare with existing methods. An application to a financial time series is also presented. [ABSTRACT FROM AUTHOR]

We investigate a self-normalized central limit theorem for a ρ-mixing stationary sequence {Xi,i⩾ 1} of random variables such thatL(x) ≔E(X21I{|X1| ⩽x}) is a slowly varying function asx→ ∞. The results obtained generalize the results of Gine, Gotze, and Mason (1997) and Mason (2005) to ρ-mixing sequences. [ABSTRACT FROM AUTHOR]

Many datasets present time-dependent variation and short-term clustering within extreme values. The extremal index is a primary measure to evaluate clustering of high values in a stationary sequence. Estimation procedures are based on the choice of a threshold and/or a declustering parameter or a block size. Here we revise several different methods and compare them through simulation. In particular, we will see that a recent declustering methodology may be useful for the popular runs estimator and for a new estimator that works under the validation of a local dependence condition. An application to real data is also presented. [ABSTRACT FROM AUTHOR]

The resurrection axioms are forcing axioms introduced recently by Hamkins and Johnstone, developing on ideas of Chalons and Veličković. We introduce a stronger form of resurrection axioms (the iterated resurrection axioms for a class of forcings and a given ordinal ), and show that implies generic absoluteness for the first-order theory of with respect to forcings in preserving the axiom, where is a cardinal which depends on ( if is any among the classes of countably closed, proper, semiproper, stationary set preserving forcings). We also prove that the consistency strength of these axioms is below that of a Mahlo cardinal for most forcing classes, and below that of a stationary limit of supercompact cardinals for the class of stationary set preserving posets. Moreover, we outline that simultaneous generic absoluteness for with respect to and for with respect to with is in principle possible, and we present several natural models of the Morse-Kelley set theory where this phenomenon occurs (even for all simultaneously). Finally, we compare the iterated resurrection axioms (and the generic absoluteness results we can draw from them) with a variety of other forcing axioms, and also with the generic absoluteness results by Woodin and the second author. [ABSTRACT FROM AUTHOR]

We investigate the relationship between weak square principles and simultaneous reflection of stationary sets. [ABSTRACT FROM AUTHOR]

Operator self-similar processes, as an extension of self-similar processes, have been studied extensively. In this work, we study limit theorems for functionals of Gaussian vectors. Under some conditions, we determine that the limit of partial sums of functionals of a stationary Gaussian sequence of random vectors is an operator self-similar process. [ABSTRACT FROM AUTHOR]

The subject matter of this paper is an integral with exponential oscillation of phase f( x) weighted by g( x) on a finite interval [α β]: When the phase f( x) has a single stationary point in (α β), an nth-order asymptotic expansion of this integral is proved for n ≥ 2: This asymptotic expansion sharpens the classical result for n = 1 by M. N. Huxley. A similar asymptotic expansion was proved by V. Blomer, R. Khan and M. Young under the assumptions that f( x) and g( x) are smooth and g( x) is compactly supported on R: In the present paper, however, these functions are only assumed to be continuously differentiable on [α β] 2 n + 3 and 2 n + 1 times, respectively. Because there are no requirements on the vanishing of g( x) and its derivatives at the endpoints α and β, the present asymptotic expansion contains explicit boundary terms in the main and error terms. The asymptotic expansion in this paper is thus applicable to a wider class of problems in analysis, analytic number theory, and other fields. [ABSTRACT FROM AUTHOR]

For a strictly stationary sequence of R + d –valued random vectors we derive functional convergence of partial maxima stochastic processes under joint regular variation and weak dependence conditions. The limit process is an extremal process and the convergence takes place in the space of R + d –valued càdlàg functions on [ 0 , 1 ] , with the Skorohod weak M 1 topology. We also show that this topology in general cannot be replaced by the stronger (standard) M 1 topology. The theory is illustrated on three examples, including the multivariate squared GARCH process with constant conditional correlations. [ABSTRACT FROM AUTHOR]

We prove a deviation bound for the maximum of partial sums of functions of -dependent sequences as defined in [2]. As a consequence, we extend the Rosenthal inequality of Rio [16] for -mixing sequences in the sense of Rosenblatt [18] to the larger class of -dependent sequences. Starting from the deviation inequality, we obtain upper bounds for large deviations and Hölderian invariance principle for the Donsker line. We illustrate our results through the example of intermittent maps of the interval, which are not -mixing in the sense of Rosenblatt. [ABSTRACT FROM AUTHOR]

In this note, we show that a stationary sequence obtained by applying a fixed deterministic function to shifts of a stationary sequence (satisfying a mild regularity condition) has a spectral density. In the multiparametric setting, we obtain a similar result for a function of a shifted i.i.d. field. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the compressible Navier–Stokes–Poisson equations with the given external force of general form in three dimensional space. Based on the weighted L 2 method and the contraction mapping principle, we prove the existence and uniqueness of stationary solutions. Then, we show the stability of solutions to the Cauchy problem near the stationary state provided that the initial perturbation is sufficiently small. Finally, the time decay rates of the solutions are obtained when the initial perturbation belongs to H ̇ − s with 0 ≤ s < 3 2 . [ABSTRACT FROM AUTHOR]

We prove that the automorphism group of a Fraïssé structure M equipped with a notion of stationary independence is universal for the class of automorphism groups of substructures of M . Furthermore, we show that this applies to certain homogeneous n -gons. [ABSTRACT FROM AUTHOR]

We prove some almost sure central limit theorems for the maxima of strongly dependent nonstationary Gaussian vector sequences under some mild conditions. The results extend the ASCLT to nonstationary Gaussian vector sequences and give substantial improvements for the weight sequence obtained by Lin et al. (Comput. Math. Appl. 62(2):635-640, ). [ABSTRACT FROM AUTHOR]

In this paper, we prove that, under some mild conditions, a time-normalized point process of exceedances by a nonstationary and strongly dependent normal sequence with a seasonal component converges in distribution to the in plane Cox process. As an application of the convergence result, we deduce two important joint limit distributions for the order statistics. [ABSTRACT FROM AUTHOR]

In this paper we investigate some properties of forcing which can be considered 'nice' in the context of singularizing regular cardinals to have an uncountable cofinality. We show that such forcing which changes cofinality of a regular cardinal, cannot be too nice and must cause some 'damage' to the structure of cardinals and stationary sets. As a consequence there is no analogue to the Prikry forcing, in terms of 'nice' properties, when changing cofinalities to be uncountable. [ABSTRACT FROM AUTHOR]

Let {Ti,i⩾ 1} be a strictly stationary sequence of associated random variables distributed asT. This paper aims to establish strong uniform consistency over a compact set with a rate of a kernel estimator of the underlying density functionfwhen the random variable of interestTis right-censored by another variableC. As a consequence, the almost sure convergence of a new smooth kernel mode estimatorof the true mode θ offwith rate is stated. [ABSTRACT FROM AUTHOR]

The previously known results about the generalization performance of ranking algorithms are mainly based on the assumption of independently and identically (i.i.d.) distributed samples. In this paper, we go beyond this limitation by investigating the generalization ability of ranking where the samples are drawn from a stationary φ -mixing sequence. The generalization bounds are established by the independent block technique and the algorithmic stability analysis. The derived results are applied to the regularized ranking algorithms with general convex losses, which extend the existing results for i.i.d. observations to the case of stationary φ -mixing samples. [ABSTRACT FROM AUTHOR]

In this paper we deal with stationary points (also known as endpoints) of nonexpansive set-valued mappings and show that the existence of such points under certain conditions follows as a consequence of the existence of approximate stationary sequences. In particular we provide abstract extensions of well-known fixed point theorems. [ABSTRACT FROM AUTHOR]

Stationary anonymous sequential games with undiscounted rewards are a special class of games that combine features from both population games (infinitely many players) with stochastic games. We extend the theory for these games to the cases of total expected reward as well as to the expected average reward. We show that in the anonymous sequential game equilibria correspond to the limits of those of related finite population games as the number of players grows to infinity. We provide examples to illustrate our results. [ABSTRACT FROM AUTHOR]

The idea of using fast sweeping methods for solving stationary systems of conservation laws has previously been proposed for efficiently computing solutions with sharp shocks. We further develop these methods to allow for a more challenging class of problems including problems with sonic points, shocks originating in the interior of the domain, rarefaction waves, and two-dimensional systems. We show that fast sweeping methods can produce higher-order accuracy. Computational results validate the claims of accuracy, sharp shock curves, and optimal computational efficiency. [ABSTRACT FROM AUTHOR]

In this paper, we develop new methods for approximating dominant eigenvector of column-stochastic matrices. We analyze the Google matrix, and present an averaging scheme with linear rate of convergence in terms of 1-norm distance. For extending this convergence result onto general case, we assume existence of a positive row in the matrix. Our new numerical scheme, the Reduced Power Method (RPM), can be seen as a proper averaging of the power iterates of a reduced stochastic matrix. We analyze also the usual Power Method (PM) and obtain convenient conditions for its linear rate of convergence with respect to 1-norm. [ABSTRACT FROM AUTHOR]

Building on early work by Stevo Todorcevic, we develop a theory of stationary subtrees of trees of successor-cardinal height. We define the diagonal union of subsets of a tree, as well as normal ideals on a tree, and we characterize arbitrary subsets of a non-special tree as being either stationary or non-stationary. We then use this theory to prove the following partition relation for trees: Main Theorem. Let $${\kappa}$$ be any infinite regular cardinal, let ξ be any ordinal such that $${2^{|\xi|} < \kappa}$$ , and let k be any natural number. ThenThis is a generalization to trees of the Balanced Baumgartner-Hajnal-Todorcevic Theorem, which we recover by applying the above to the cardinal $${(2^{< \kappa})^{+}}$$ , the simplest example of a non- $${(2^{< \kappa})}$$ -special tree. As a corollary, we obtain a general result for partially ordered sets: Theorem. Let $${\kappa}$$ be any infinite regular cardinal, let ξ be any ordinal such that $${2^{|\xi|} < \kappa}$$ , and let k be any natural number. Let P be a partially ordered set such that $${P \rightarrow (2^{< \kappa})^{1}_{2^{< \kappa}} }$$ . Then [ABSTRACT FROM AUTHOR]

For a long time, the bilevel programming problem has essentially been considered as a special case of mathematical programs with equilibrium constraints, in particular when the so-called KKT reformulation is in question. Recently though, this widespread believe was shown to be false in general. In this paper, other aspects of the difference between both problems are revealed as we consider the KKT approach for the nonsmooth bilevel program. It turns out that the new inclusion (constraint) which appears as a consequence of the partial subdifferential of the lower-level Lagrangian (PSLLL) places the KKT reformulation of the nonsmooth bilevel program in a new class of mathematical program with both set-valued and complementarity constraints. While highlighting some new features of this problem, we attempt here to establish close links with the standard optimistic bilevel program. Moreover, we discuss possible natural extensions for C-, M-, and S-stationarity concepts. Most of the results rely on a coderivative estimate for the PSLLL that we also provide in this paper. [ABSTRACT FROM AUTHOR]

In 1983, N. Herrndorf proved that for a ϕ-mixing sequence satisfying the central limit theorem and lim infn→∞σn2/n>0, the weak invariance principle takes place. The question whether for strictly stationary sequences with finite second moments and a weaker type α, β, ρ of mixing the central limit theorem implies the weak invariance principle remained open. We construct a strictly stationary β-mixing sequence with finite moments of any order and linear variance for which the central limit theorem takes place but not the weak invariance principle. [ABSTRACT FROM AUTHOR]

The paper is concerned with the numbers of non-occurring values in intervals of a stationary sequence of m-dependent random variables with N outcomes. These numbers are shown to be asymptotically joint normally distributed, provided that the number N and the lengths of intervals tend to infinity with the same asymptotic order of growth. [ABSTRACT FROM AUTHOR]

We get stationary solutions of a free stochastic partial differential equation. As an application, we prove equality of non-microstate and microstate free entropy dimensions under a Lipschitz like condition on conjugate variables, assuming also the von Neumann algebra Rω embeddable. This includes an N-tuple of q-Gaussian random variables e.g. for ∣q∣N ≤ 0.13. [ABSTRACT FROM AUTHOR]

We derive exponential upper bounds for the distribution tails of multiple stochastic integrals of bounded nonrandom functions. In this paper we consider integrating processes from certain wide classes. Some important examples of integrating processes are given. Multiple stochastic integrals with respect to increments of such processes arise in statistical applications. [ABSTRACT FROM AUTHOR]

This paper is concerned with n -species model of facultative mutualism in random environments. The environment variability in this study is characterized with both white noise and color noise modeled by Markovian switching. We established new sufficient conditions that ensuring that the system model is positive recurrent. We also showed the existence of a unique ergodic stationary distribution. The presented results are demonstrated by numerical simulations. [ABSTRACT FROM AUTHOR]

In the seminal contribution [R.A. Davis,Maxima and minima of stationary sequences, Ann. Probab. 7(3) (1979), pp. 453–460.] the joint weak convergence of maxima and minima of weakly dependent stationary sequences is derived under some mild asymptotic conditions. In this paper we address additionally the case of incomplete samples assuming that the average proportion of incompleteness converges in probability to some random variable. We show the joint weak convergence of the maxima and the minima of both complete and incomplete samples. It turns out that the maxima and the minima are asymptotically independent whenis a deterministic constant. [ABSTRACT FROM PUBLISHER]

We consider $$GI/Ph/n+M$$ parallel-server systems with a renewal arrival process, a phase-type service time distribution, $$n$$ homogenous servers, and an exponential patience time distribution with positive rate. We show that in the Halfin-Whitt regime, the sequence of stationary distributions corresponding to the normalized state processes is tight. As a consequence, we establish an interchange of heavy-traffic and steady-state limits for $$GI/Ph/n+M$$ queues. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we study the non-existence of non-constant steady state (i.e., stationary pattern) for a Chemotaxis model with the volume-filling effect and logistic cell growth. We establish the critical value of the chemotactic coefficient between the existence and the non-existence of stationary pattern. The proofs mainly rely on the Maximum Principle, the Implicit Function Theorem and the Finite Covering Theorem. This work is a supplement and perfection of the known reference. [Copyright &y& Elsevier]

We study exact stationary properties of the one-dimensional Kardar-Parisi-Zhang (KPZ) equation by using the replica approach. The stationary state for the KPZ equation is realized by setting the initial condition the two-sided Brownian motion (BM) with respect to the space variable. Developing techniques for dealing with this initial condition in the replica analysis, we elucidate some exact nature of the height fluctuation for the KPZ equation. In particular, we obtain an explicit representation of the probability distribution of the height in terms of the Fredholm determinants. Furthermore from this expression, we also get the exact expression of the space-time two-point correlation function. [ABSTRACT FROM AUTHOR]

Let (Xn) denote an independent and identically distributed random sequence. Let $S_n = \sum_{k = 1}^{n}X_{k}$ and Mn = max{X1, ..., Xn} be its partial sum and maximum. Suppose that some of the random variables of X1, X2,... can be observed and denote by $\widetilde{M}_n$ the maximum of observed random variables from the set {X1, ..., Xn}. In this paper, we consider the joint limiting distribution of $(\widetilde{M}_n, M_n, S_n)$ and the almost sure central limit theorems related to the random vector $( \widetilde{M}_n, M_n, S_n)$. Furthermore, we extend related results to weakly dependent stationary Gaussian sequences. [ABSTRACT FROM AUTHOR]

Abstract: Relative stability results for weakly dependent and strongly mixing strictly stationary sequences are established. As a consequence, some infinite memory models, including ARCH(1) processes, are relatively stable. [Copyright &y& Elsevier]

Static forecasting of stationary and ergodic time series is considered, i.e., inference of the conditional expectation of the response variable at time zero given the infinite past. It is shown that the mean squared error of a combination of suitably defined localized least squares estimates converges to zero for all distributions where the response variable is square integrable. [ABSTRACT FROM AUTHOR]

The Kalman-Bucy filter that can be modeled by computer statistical design is constructed for stochastic dynamic systems with Poisson perturbations. It is proved that a stationary filter coincides with the Wiener filter for the optimal mean-square filtering of stationary sequences in the absence of Poisson perturbations. [ABSTRACT FROM AUTHOR]

This article concerns radially symmetric positive solutions of second-order quasilinear elliptic systems. In terms of the growth of the variable potential functions, we establish conditions such that the solutions are either bounded or blow up at infinity. [ABSTRACT FROM AUTHOR]

Discrete-time renewal sequences play a fundamental role in the theory of stochastic processes. This article considers periodic versions of such processes; specifically, the length of an interrenewal is allowed to probabilistically depend on the season at which it began. Using only elementary renewal and Markov chain techniques, computational and limiting aspects of periodic renewal sequences are investigated. We use these results to construct a time series model for a periodically stationary sequence of integer counts. [ABSTRACT FROM PUBLISHER]

The authors have elaborated mathematical models and information technologies for the experimental-analytical determination of stress-strain state and ultimate accumulated strain in a material on a barreled side surface of a cylindrical specimen under edge compression. A model that allows one to predict the ultimate accumulated plastic strain has been introduced in the form of an analytic relationship between plastic strain components which represents the specified nonstationary deformation conditions. [ABSTRACT FROM AUTHOR]

In this paper, using a Brownian motion we define a new type of covariance for random vectors with a finite second moment. The advantage of Brownian covariance is in the fact that it is equal to zero if and only if the random vectors are independent. We can apply Brownian covariance to random vectors, generally speaking, of different sizes if it is invariant with respect to rotations of axes where the data are given. If, in the definition of Brownian covariance, we replace Brownian motion by an identical function, then we obtain a modulus of the classical Pearson covariance coefficient, and therefore, Brownian covariance generalizes the classical. Brownian covariance is applied to the proof of necessary and sufficient conditions for the validity of the central limit theorem for random sequences which are stationary in a narrow sense. [ABSTRACT FROM AUTHOR]