Related papers: Convergence analysis of some multivariate Markov c…
We show that the product or convex combination of two Markov operators with equivalent stationary measures need not have a stationary measure from the same measure class. More specifically, we exhibit examples of a hitherto undescribed…
In this paper we investigate the continuum limits of a class of Markov chains. The investigation of such limits is motivated by the desire to model very large networks. We show that under some conditions, a sequence of Markov chains…
Stabilization of non-stationary linear systems over noisy communication channels is considered. Stochastically stable sources, and unstable but noise-free or bounded-noise systems have been extensively studied in information theory and…
We prove the existence and uniqueness of a quasi-stationary distribution for three stochastic processes derived from the model of Muller's ratchet. This model was invented with the aim of evaluating the limitations of an asexual…
We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state…
In this work, we focus on the stationary analysis of a specific class of continuous time Markov-modulated reflected random walks in the quarter plane with applications in the modelling of two-node Markov-modulated queueing networks with…
We construct strong stationary dual chains for Ising model on a circle, non-symmetric random walk on square lattice and a random walk on hypercube. The strong stationary dual chains are all sharp and have the same state space as original…
In this work we generalize Polya urn schemes with possibly infinitely many colors and extend the earlier models described in [4, 5, 7]. We provide a novel and unique approach of representing the observed sequence of colors in terms a…
A classical problem for Markov chains is determining their stationary (or steady-state) distribution. This problem has an equally classical solution based on eigenvectors and linear equation systems. However, this approach does not scale to…
We analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions are not equivalent. However,…
We prove stochastic stability of chaotic maps for a general class of Markov random perturbations (including singular ones) satisfying some kind of mixing conditions. One of the consequences of this statement is the proof of Ulam's…
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…
We consider continuous-time Markov chains which display a family of wells at the same depth. We provide sufficient conditions which entail the convergence of the finite-dimensional distributions of the order parameter to the ones of a…
We study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuous-time Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems…
The upper extremes of a Markov chain with regulary varying stationary marginal distribution are known to exhibit under general conditions a multiplicative random walk structure called the tail chain. More generally, if the Markov chain is…
This paper presents an elementary proof of stochastic stability of a discrete-time reversible Markov chain starting from a Foster-Lyapunov drift condition. Besides its relative simplicity, there are two salient features of the proof: (i) it…
Mostof the existing literature on supervised machine learning problems focuses on the case when the training data set is drawn from an i.i.d. sample. However, many practical problems are characterized by temporal dependence and strong…
The first paper in this series introduced a \emph{short-to-long mixing} condition that captures mean-field GOE/GUE edge universality in the supercritical sparsity regime, for symmetric/Hermitian random matrices with independent entries and…
In many branches of engineering, Banach contraction mapping theorem is employed to establish the convergence of certain deterministic algorithms. Randomized versions of these algorithms have been developed that have proved useful in…
The paper presents a generalization of the local limit theorem on the convergence of inhomogeneous Markov chains to the diffusion limit for the case where the corresponding process coefficients satisfy weak regularity conditions and…