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Accurate forecasting of high-resolution particulate matter 2.5 (PM2.5) levels is essential for the development of public health policy. However, datasets used for this purpose often contain missing observations. This study presents a two-stage approach to handle this problem. The first stage is a multivariate spatial time series (MSTS) model, used to generate forecasts for the sampled spatial units and to impute missing observations. The MSTS model utilizes the similarities between the temporal patterns of the time series of the spatial units to impute the missing data across space. The second stage is the high-resolution prediction model, which generates predictions that cover the entire study domain. The second stage faces the big N problem giving rise to complex memory and computational problems. As a solution to the big N problem, we propose a Gaussian Markov random field (GMRF) for innovations with the Matérn covariance matrix obtained from the corresponding Gaussian field (GF) matrix by means of the stochastic partial differential equation (SPDE) method and the finite element method (FEM). For inference, we propose Bayesian statistics and integrated nested Laplace approximation (INLA) in the R-INLA package. The above approach is demonstrated using daily data collected from 13 PM2.5 monitoring stations in Jakarta Province, Indonesia, for 1 January–31 December 2022. The first stage of the model generates PM2.5 forecasts for the 13 monitoring stations for the period 1–31 January 2023, imputing missing data by means of the MSTS model. To capture temporal trends in the PM2.5 concentrations, the model applies a first-order autoregressive process and a seasonal process. The second stage involves creating a high-resolution map for the period 1–31 January 2023, for sampled and non-sampled spatiotemporal units. It uses the MSTS-generated PM2.5 predictions for the sampled spatiotemporal units and observations of the covariate's altitude, population density, and rainfall for sampled and non-samples spatiotemporal units. For the spatially correlated random effects, we apply a first-order random walk process. The validation of out-of-sample forecasts indicates a strong model fit with low mean squared error (0.001), mean absolute error (0.037), and mean absolute percentage error (0.041), and a high R² value (0.855). The analysis reveals that altitude and precipitation negatively impact PM2.5 concentrations, while population density has a positive effect. Specifically, a one-meter increase in altitude is linked to a 7.8% decrease in PM2.5, while a one-person increase in population density leads to a 7.0% rise in PM2.5. Additionally, a one-millimeter increase in rainfall corresponds to a 3.9% decrease in PM2.5. The paper makes a valuable contribution to the field of forecasting high-resolution PM2.5 levels, which is essential for providing detailed, accurate information for public health policy. The approach presents a new and innovative method for addressing the problem of missing data and high-resolution forecasting. [ABSTRACT FROM AUTHOR]

In this paper, we describe categories whose objects are chains of stochastic vectors/stochastic matrices with morphisms that are appropriate maps between such objects with functors in this category are chain maps. The chain categories are interesting and significant in several situations such as Markov chains, stochastic processes, and queuing theory. Here we provide examples of chain categories and discuss many interesting properties of such categories. [ABSTRACT FROM AUTHOR]

We study genetic coalgebras whose comultiplications, equivalently, their associated cubic stochastic matrices, are skewed by the simultaneous action of three square stochastic matrices. A two-fold, algebraic and stochastic, approach is pursued. First, we detail the structural consequences on the algebraic structure, to then tackle the underlying stochastic processes. [ABSTRACT FROM AUTHOR]

Dependency plays a key role in the design stage of multi-component manufacturing systems. To capture stochastic dependencies between subsystems, this paper considers a load-sharing k -out-of- n : G system which contains non-identical multi-state subsystems. The state evolution of each subsystem follows a continuous-time homogeneous Markov chain. Most existing research on k -out-of- n : G systems focuses on independent subsystems. However, a subsystem failure usually leads to a higher failure rate for each surviving subsystem within the system. This paper aims to study the interaction among subsystems and analyse the system reliability performance. The transition rate matrix for a given subsystem is assumed to depend on the total number of the remaining surviving subsystems, which can be represented as the sum of a baseline transition rate matrix and a stochastic dependency matrix. This paper proves that the transition rate matrix of the system is the generalised Kronecker sum of transition rate matrices of subsystems, and develops an explicit method to calculate the generalised Kronecker sum. The theory of aggregated stochastic processes is employed to obtain closed-form formulas for reliability indexes. A case study of multi-engine aircraft systems is provided where numerical examples are given to illustrate the developed model and obtained results. [ABSTRACT FROM AUTHOR]

In this article, we propose the shifted Legendre polynomial solutions for anti-persistent process based stochastic integral equations. The operational matrices for stochastic integration and fractional stochastic integration are efficiently generated using the properties of shifted Legendre polynomials. In addition, the original problem can be reduced to a system of simultaneous equations with (N + 1) unknowns in the function approximation. By solving the given stochastic integral equations, we obtain numerical solutions. The proposed method's convergence is derived in terms of the error function's expectation, and the upper bound of the error in L² norm is also discussed in detail. The applicability of this methodology is demonstrated using numerical examples and the solution's quality is statistically validated by comparing it with the exact solution. [ABSTRACT FROM AUTHOR]

Factor models have been widely used in recent years to model high‐dimensional spatio‐temporal data. However, the validity of employing factor models in a specific application has received less attention. This article proposes test statistics for testing the symmetry in cross‐correlation matrices of a high‐dimensional stochastic process implied by exact factor models. A rejection of symmetry indicates that the use of an exact factor model is questionable. Both simulations and real examples are used to demonstrate the applications and to study the finite‐sample performance of the proposed test statistics. Empirical results show that the proposed test statistics are effective in identifying cases where exact factor models are not appropriate, providing valuable guidance for choosing factor models in a high‐dimensional setting. [ABSTRACT FROM AUTHOR]

We study the Brownian motion on the non-compact Grassmann manifold $\frac {\textbf {U}(n-k,k)} {\textbf {U}(n-k)\textbf {U}(k)}$ and some of its functionals. The key point is to realize this Brownian motion as a matrix diffusion process, use matrix stochastic calculus and take advantage of the hyperbolic Stiefel fibration to study a functional that can be understood in that setting as a generalized stochastic area process. In particular, a connection to the generalized Maass Laplacian of the complex hyperbolic space is presented and applications to the study of Brownian windings in the Lie group $\textbf {U}(n-k,k)$ are then given. [ABSTRACT FROM AUTHOR]

We develop new techniques involving group symmetries and complex analysis to obtain exact solutions for the transition probabilities of the M/M/1/k queueing process. These methods are based on the underlying Markovian structure of these random processes and do not involve any generating functions, Laplace transforms, or advanced special functions. Our techniques exploit the intrinsic group symmetries for both the state spaces and the matrix generators of the Markov processes related to the M/M/1/k queue. These results complement and extend the previous transient solutions given by Takács (Introduction to the theory of queues. University texts in the mathematical sciences, Oxford University Press, New York, 1962). Much of the inspiration for this work comes from viewing this queueing process as a fundamental Markovian model for the dynamics of a bike sharing station. The exact transient analysis for a related stopped version of this process can be used to address fundamental decision-making issues for managing bike-sharing services. [ABSTRACT FROM AUTHOR]

This paper investigates the controllability of Markovian jump Boolean control networks (MJBCNs) by using graphical approach. To solve this problem, a deterministic directed graph is constructed to describe the stochastic evolutionary process of the considered MJBCN under the framework of semi-tensor product of matrices. Then, combining with breadth-first search, the special subgraph with breadth-first tree as the principal part is obtained. Based on this, the necessary and sufficient conditions to verify the controllability of MJBCNs are deduced, and the problem of determining the minimal controllable time is solved completely. Subsequently, two examples are given to illustrate the validity and correctness of the method. [ABSTRACT FROM AUTHOR]

• A GHW-based method to simulate fully nonstationary stochastic vector processes is proposed. • This method improves the computing efficiency of vector process simulation by reducing the numbers of random variables. • The relationship between the cross spectrum matrix and the GHW coefficients of vector process is derived. Currently, the most common approach to simulate stochastic vector processes for structural dynamic reliability analysis is the Spectral Representation Method (SRM), characterized by a superposition of amplitude-modulated trigonometric functions with random phase angles. However, to represent the vector processes completely, the SRM requires the sampling of a large number of independent random variables, that may cause a large amount of computational cost for the time history sample generation and structural reliability calculation. To reduce the number of random variables, this paper presents a method based on the generalized harmonic wavelet (GHW) to simulate fully nonstationary stochastic vector processes. First, the relationship between the GHW coefficients and the evolutionary cross spectrum matrix of the stochastic vector process is derived. Then, based on the inverse GHW transform, a general simulation formula by superposing GHWs is proposed. The corresponding simplified method which requires less independent random variables is also presented. At last, a numerical case study is provided to emphasize the efficiency of the proposed method. The result indicates that, due to the localization of the energy distribution of the GHW in the time–frequency domain, the proposed method could generate the stochastic vector process samples using less components and is more efficient than the SRM. This method has high potential for application in the Monte Carlo simulation of spatially variable seismic ground motions or wind velocities for structural dynamic reliability analysis. [ABSTRACT FROM AUTHOR]

This paper is involved with synchronization of fractional order stochastic systems in finite dimensional space, and we have tested its time response and stochastic chaotic behaviors. Firstly, we give a representation of solution for a stochastic fractional order chaotic system. Secondly, some useful sufficient conditions are investigated by using matrix type Mittag-Leffler function, Jacobian matrix via stochastic process, stability analysis and feedback control technique to assure the synchronization of stochastic error system. Thereafter, numerical illustrations are provided to verify the theoretical parts. [ABSTRACT FROM AUTHOR]

Data centers are increasingly using high-speed circuit switches to cope with the growing demand and reduce operational costs. One of the fundamental tasks of circuit switches is to compute a sparse collection of switching configurations to support a traffic demand matrix. Such a problem has been addressed in the literature with variations of the approach proposed by Birkhoff in 1946 to decompose a doubly stochastic matrix exactly. However, the existing methods are heuristic and do not have theoretical guarantees on how well a collection of switching configurations (i.e., permutations) can approximate a traffic matrix (i.e., a scaled doubly stochastic matrix). In this paper, we revisit Birkhoff’s approach and make three contributions. First, we establish the first theoretical bound on the sparsity of Birkhoff’s algorithm (i.e., the number of switching configurations necessary to approximate a traffic matrix). In particular, we show that by using a subset of the admissible permutation matrices, Birkhoff’s algorithm obtains an $\epsilon $ -approximate decomposition with at most $O(\log (1 / \epsilon))$ permutations. Second, we propose a new algorithm, Birkhoff+, which combines the wealth of Frank-Wolfe with Birkhoff’s approach to obtain sparse decompositions in a fast manner. And third, we evaluate the performance of the proposed algorithm numerically and study how this affects the performance of a circuit switch. Our results show that Birkhoff+ is superior to previous algorithms in terms of throughput, running time, and number of switching configurations. [ABSTRACT FROM AUTHOR]

In this paper, we show how questions about operator algebras constructed from stochastic matrices motivate new results in the study of harmonic functions on Markov chains. More precisely, we characterize the coincidence of conditional probabilities in terms of (generalized) Doob transforms, which then leads to a stronger classification result for the associated operator algebras in terms of spectral radius and strong Liouville property. Furthermore, we characterize the noncommutative peak points of the associated operator algebra in a way that allows one to determine them from inspecting the matrix. This leads to a concrete analogue of the maximum modulus principle for computing the norm of operators in the ampliated operator algebras. [ABSTRACT FROM AUTHOR]

We establish bounds for Schatten norms of mean squared errors of plug-in estimators of matrix functions that are dimension-independent and optimal with respect to key parameters. We also obtain similar bounds for bias approximation errors that significantly sharpen existing bounds and extend their range of applicability. When applied to estimators of covariance matrix functions, our bounds reduce dimensional dependence of the sample size that ensures smallness of the estimation errors. [ABSTRACT FROM AUTHOR]

In this paper, we first give an overview of doubly stochastic interval matrices. Then, we present some theories about the interval linear system whose coefficient matrix is doubly stochastic interval matrix. Also, we give an outer estimation for the solution set of these systems. [ABSTRACT FROM AUTHOR]

In this article, we propose an efficient heterogeneous change detection algorithm based on stochastic distance measure between two $\mathcal {G}_{d}^{0}$ distributions. Due to its flexibility and simplicity, the matrix-variate $\mathcal {G}_{d}^{0}$ distribution has been successfully used to model the multilook polarimetric synthetic aperture radar (PolSAR) data and has been tested for classification, segmentation, and image analysis. Concretely, closed-form expressions for the Kullback–Leibler, Renyi of order $\beta $ , Bhattacharyya, and Hellinger distances are provided to compute the stochastic distance between $\mathcal {G}_{d}^{0}$ distributions. In this context, we resort to the expectation–maximization (EM) to estimate accurately with low complexity for the parameters of the probability distribution of the two multilook polarimetric covariance matrices to be compared. Finally, the performance of the method is compared firstly to the performance of other known distributions, such as the scaled complex Wishart distribution, and secondly to other known statistical tests using simulated and real multilook PolSAR data. [ABSTRACT FROM AUTHOR]

This letter addresses the initialization problem of power systems modeled as (SDAEs) and proposes a novel efficient initialization method. The method involves finding the co-variance matrix for the system state variables and initializing the stochastic state variables of the system randomly based on their probability distribution. Deterministic states and algebraic variables are then initialized based on the initial stochastic processes and the system co-variance matrix. The proposed method is illustrated through Monte Carlo simulations of a one-machine infinite-bus system and its numerical performance discussed through a dynamic 1479-bus model of the all-island Irish transmission system. It is shown that by utilizing the proposed method the computation time needed for the Monte Carlo simulations of the system can be reduced significantly compared to other initialization methods used in the literature. [ABSTRACT FROM AUTHOR]

This paper considers a novel multi-agent linear stochastic approximation algorithm driven by Markovian noise and general consensus-type interaction, in which each agent evolves according to its local stochastic approximation process which depends on the information from its neighbors. The interconnection structure among the agents is described by a time-varying directed graph. While the convergence of consensus-based stochastic approximation algorithms when the interconnection among the agents is described by doubly stochastic matrices (at least in expectation) has been studied, less is known about the case when the interconnection matrix is simply stochastic. For any uniformly strongly connected graph sequences whose associated interaction matrices are stochastic, the paper derives finite-time bounds on the mean-square error, defined as the deviation of the output of the algorithm from the unique equilibrium point of the associated ordinary differential equation. For the case of interconnection matrices being stochastic, the equilibrium point can be any unspecified convex combination of the local equilibria of all the agents in the absence of communication. Both the cases with constant and time-varying step-sizes are considered. In the case when the convex combination is required to be a straight average and interaction between any pair of neighboring agents may be uni-directional, so that doubly stochastic matrices cannot be implemented in a distributed manner, the paper proposes a push-sum-type distributed stochastic approximation algorithm and provides its finite-time bound for the time-varying step-size case by leveraging the analysis for the consensus-type algorithm with stochastic matrices and developing novel properties of the push-sum algorithm. Distributed temporal difference learning is discussed as an illustrative application. [ABSTRACT FROM AUTHOR]

We consider Markov processes of cubic stochastic (in a fixed sense) matrices which are also called quadratic stochastic process (QSPs). A QSP is a particular case of a continuous-time dynamical system whose states are stochastic cubic matrices satisfying an analogue of the Kolmogorov-Chapman equation (KCE). Since there are several kinds of multiplications between cubic matrices we have to fix first a multiplication and then consider the KCE with respect to the fixed multiplication. Moreover, the notion of stochastic cubic matrix also varies depending on the real models of application. The existence of a stochastic (at each time) solution to the KCE provides the existence of a QSP. In this paper, our aim is to construct QSPs for two specially chosen notions of stochastic cubic matrices and two multiplications of such matrices (known as Maksimov's multiplications). We construct a wide class of QSPs and give some time-dependent behavior of such processes. We give an example with applications to the Biology, constructing a QSP which describes the time behavior (dynamics) of a population with the possibility of twin births. [ABSTRACT FROM AUTHOR]

The transition probabilities of jumps between operational modes of discrete-time Markov(ian) jump linear systems (dtMJLSs) are generally considered to be time-invariant, certain, and often completely known in the majority of dedicated studies. Still, in most real cases the transition probability matrix (TPM) cannot be computed exactly and is time-varying. In this article, we take into account the uncertainty and time-variance of the jump parameters by considering the underlying Markov chain as polytopic and time-inhomogeneous, i.e., its TPM is varying over time with variations that are arbitrary within a polytopic set of stochastic matrices. We show that the conditions used for time-homogeneous dtMJLSs are not enough to ensure the stability of the time-inhomogeneous system, and that perturbations on values of the TPM can make a stable system unstable. We present necessary and sufficient conditions for mean square stability (MSS) of polytopic time-inhomogeneous dtMJLSs, prove that deciding MSS on such systems is NP-hard and that MSS is equivalent to exponential MSS and to stochastic stability. We also derive necessary and sufficient conditions for robust MSS of dtMJLSs affected by polytopic uncertainties on transition probabilities and bounded disturbances. [ABSTRACT FROM AUTHOR]

We discuss the limiting spectral density of real symmetric random matrices. In contrast to standard random matrix theory, the upper diagonal entries are not assumed to be independent, but we will fill them with the entries of a stochastic process. Under assumptions on this process which are satisfied, e.g., by stationary Markov chains on finite sets, by stationary Gibbs measures on finite state spaces, or by Gaussian Markov processes, we show that the limiting spectral distribution depends on the way the matrix is filled with the stochastic process. If the filling is in a certain way compatible with the symmetry condition on the matrix, the limiting law of the empirical eigenvalue distribution is the well-known semi-circle law. For other fillings we show that the semi-circle law cannot be the limiting spectral density. [ABSTRACT FROM AUTHOR]

Abstract We consider weighted negatively reinforced urn schemes with finitely many colours. An urn scheme is called negatively reinforced, if the selection probability for a colour is proportional to the weight w of the colour proportion, where w is a non-increasing function. Under certain assumptions on the random replacement rule and the weight function w , such as, w is differentiable and w (0) < ∞ , we obtain almost sure convergence of the random configuration of the urn model. In particular, we show that if either the number of colours are sufficiently large or if the limiting replacement matrix is a doubly stochastic matrix with diagonal entries more than 1/2, the random configuration of the urn converges to the uniform vector almost surely and the asymptotic normality holds. [ABSTRACT FROM AUTHOR]

In this article, we focus upon a family of matrix valued stochastic processes and study the problem of determining the smallest time such that their Laplace transforms become infinite. In particular, we concentrate upon the class of Wishart processes, which have proved to be very useful in different applications by their ability in describing non-trivial dependence. Thanks to this remarkable property we are able to explain the behavior of the explosion times for the Laplace transforms of the Wishart process and its time integral in terms of the relative importance of the involved factors and their correlations. [ABSTRACT FROM AUTHOR]

For any primitive matrix M ∈ R n × n with positive diagonal entries, we prove the existence and uniqueness of a positive vector x = ( x 1 , … , x n ) t such that M x = ( 1 x 1 , … , 1 x n ) t . The contribution of this note is to provide an alternative proof of a result of Brualdi et al. (1966) [1] on the diagonal equivalence of a nonnegative matrix to a stochastic matrix. [ABSTRACT FROM AUTHOR]

This article presents a technique for combining two doubly stochastic matrices with known spectra to create a new matrix. As application of this, we obtain a recursive method for constructing doubly stochastic matrices for the inverse eigenvalue problem and find new sufficient conditions for this problem. In addition, we improve the Soules' condition. [ABSTRACT FROM AUTHOR]

This paper proposes a stochastic model predictive control (MPC) approach to optimize the fuel consumption in a vehicle following context. The practical solution of that problem requires solving a constrained moving horizon optimal control problem using a short-term prediction of the preceding vehicle’s velocity. In a deterministic framework, the prediction errors lead to constraint violations and to harsh control reactions. Instead, the suggested method considers errors, and limits the probability of a constraint violation. A conditional linear Gauss model is developed and trained with real measurements to estimate the probability distribution of the future velocity of the preceding vehicle. The prediction model is used to evaluate two different stochastic MPC approaches. On the one hand, an MPC with individual chance constraints is applied. On the other hand, samples are drawn from the conditional Gaussian model and used for a scenario-based optimization approach. Finally, both developed control strategies are evaluated and compared against a standard deterministic MPC. The evaluation of the controllers shows a significant reduction of the fuel consumption compared with standard adaptive cruise control algorithms. [ABSTRACT FROM AUTHOR]

In this work we prove that if Hn = [hij]nxn is the well-known Helmert matrix, then Pn = [hij²]nxn is a regular doubly stochastic matrix. Also, we show that the Markov chain by stochastic matrix Pn is an ergodic chain. Afterwards, we prove that limk→∞ Pnk = 1/n[1]nxn, which is the stationary distribution for the stochastic matrix Pn. [ABSTRACT FROM AUTHOR]

As the power industry considers moving from a deterministic paradigm to a stochastic one to clear the day-ahead market in systems with significant stochastic production, the following question arises: how should a stochastic clearing algorithm be formulated? Our analyses indicate that a three-stage stochastic approach is clearly superior to a two-stage one. To show this, we propose a model that includes three stages: the first one represents the day-ahead market, the second stage, the intraday market, and the third one, the real-time operation. The objective is to clear the day-ahead market, but with a prognosis of the future: the intraday market and the real-time operation. To assess the impact of the intraday market on the day-ahead outcomes, we compare the results obtained from the proposed model with those of a simpler but more common two-stage model, which represents the day-ahead market and the real-time operation. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of distributed stochastic approximation in multiagent systems. The algorithm under study consists of two steps: A local stochastic approximation step and a diffusion step, which drives the network to a consensus. The diffusion step uses row-stochastic matrices to weight the network exchanges. As opposed to previous works, exchange matrices are not supposed to be doubly stochastic, and may also depend on the past estimate. We prove that nondoubly stochastic matrices generally influence the limit points of the algorithm. Nevertheless, the limit points are not affected by the choice of the matrices provided that the latter are doubly stochastic in expectation. This conclusion legitimates the use of broadcast-like diffusion protocols, which are easier to implement. Next, by means of a central limit theorem, we prove that doubly stochastic protocols perform asymptotically as well as centralized algorithms and we quantify the degradation caused by the use of nondoubly stochastic matrices. Throughout this paper, a special emphasis is put on the special case of distributed nonconvex optimization as an illustration of our results. [ABSTRACT FROM PUBLISHER]

As a generalization of the scrambling index and the exponent, m-competition index has been widely applied to stochastic matrices, food webs and memoryless communication systems in recent years. For a positive integer m, where 1 ≤ m ≤ n , the m-competition index (generalized competition index) of a primitive digraph D of order n is the smallest positive integer k such that for every pair of vertices x and y, there exist m distinct vertices v1 , v2...,, vm such that there exist walks of length k from x to v. and from y to vi for 1 ≤ i ≤ m . By analyzing the structure of θ-graphs (theta graphs) and using enumeration investigation methods, them-competition indices of primitive θ-graphs are studied and an upper bound is provided. Moreover, some corresponding extremal θ-graphs are characterized. [ABSTRACT FROM AUTHOR]

The repeated measures ANOVA is being used in the study of longitudinal data. In its standard form, the method requires full data. In practice, this is not always possible. In this paper, we consider an approach, in which the missing data are neither ignored nor are imputed. The incomplete data result in biased estimations of the time mean. This bias consists of the individual and the group components which are constructed using sequences of the regular stochastic matrices. The group adjustment is necessary in cases of the different proportion of missing values in compared groups. [ABSTRACT FROM AUTHOR]

We characterize evolutionary operators acting on coalgebras with genetic realization modeling the backwards genetic inheritance in Mendelian genetic systems. This characterization is made in terms of the different slices of the cubic stochastic matrix of type (1,2) given by the transition probabilities defining the genetic coalgebra comultiplication. We use the obtained characterization to describe all possible equilibrium states a genetic population can reach when tracing the genetic information one generation back. [ABSTRACT FROM AUTHOR]

• The simulation of non-Gaussian stochastic vector fields is addressed. • The traditional Cholesky decomposition-based iterative method is considered. • A novel eigenvalue-based iterative simulation method is proposed. • The proposed method exhibits several advantages over the traditional method. The generation of sample functions of stochastic fields or processes is a prerequisite to use the Monte Carlo method in stochastic mechanics and structural reliability analysis. When it comes to non-Gaussian characteristics such as the spatial variability of material or structural properties, the simulation of multi-dimensional non-Gaussian stochastic vector fields becomes necessary. However, the conventional Cholesky decomposition-based iterative simulation method requires three times of decomposition operations at each iteration and a complex procedure of random shuffle, which inevitably augment the model complexity. To this end, this study develops a novel eigenvalue-based iterative simulation method which only requires one decomposition operation in the whole simulation process. Central to this method is to represent the cross power spectral density matrix with its eigenvalue matrix during the iteration procedure, which avoids the cumbersome Cholesky decomposition and random shuffle procedure. Meanwhile, it can yield unique convergence result and present a powerful ability in addressing cases with the complex-valued spectral matrix. Numerical example demonstrates that the proposed method has a similar accuracy as that of the Cholesky decomposition-based iterative simulation method. Meanwhile, the estimated cumulative distribution function from one simulated sample and the estimated ensemble correlation function from 1000 simulated samples are all consistent with their respective targets. In addition, the sensitive analysis is performed to demonstrate that the proposed method has a relatively wide applicability. Therefore, this method may have a great potential to simulate multi-dimensional homogeneous non-Gaussian stochastic vector fields in practice. [ABSTRACT FROM AUTHOR]

A square matrix is called stochastic (or row-stochastic) if it is non-negative and has each row sum equal to unity. Here, we constitute an eigenvalue localization theorem for a stochastic matrix, by using its principal submatrices. As an application, we provide a suitable bound for the eigenvalues, other than unity, of the Randić matrix of a connected graph. [ABSTRACT FROM AUTHOR]

Problems similar to Ann. Prob. 22 () 424-430 and J. Appl. Prob. 23 () 1019-1024 are considered here. The limit distribution of the sequence X X⋯ X, where ( X) is a sequence of i.i.d. 2 × 2 stochastic matrices with each X distributed as μ, is identified here in a number of discrete situations. A general method is presented and it covers the cases when the random components C and D (not necessarily independent), ( C, D) being the first column of X, have the same (or different) Bernoulli distributions. Thus ( C, D) is valued in {0, r}, where r is a positive real number. If for a given positive real r, with $0

Parrondo's paradox involves two losing processes producing a winning outcome. We analyze the paradox with an original and novel method in which we start with one process and seek to construct a complementary process to achieve the paradox. We then derive a general condition for the classical Parrondo game to have a complementary process. Numerical simulation predicts that approximately two-thirds of such losing games satisfy the required condition. This suggests the common occurrence of the paradox, indicative of many potentially undiscovered applications in real-life scenarios involving stochastic processes. [ABSTRACT FROM AUTHOR]

We propose new measures of shared information, unique information and synergistic information that can be used to decompose the mutual information of a pair of random variables (Y,Z) with a third random variable X. Our measures are motivated by an operational idea of unique information, which suggests that shared information and unique information should depend only on the marginal distributions of the pairs (X,Y) and (X,Z). Although this invariance property has not been studied before, it is satisfied by other proposed measures of shared information. The invariance property does not uniquely determine our new measures, but it implies that the functions that we define are bounds to any other measures satisfying the same invariance property. We study properties of our measures and compare them to other candidate measures. [ABSTRACT FROM AUTHOR]