Related papers: Time inhomogeneous Markov chains with wave-like be…

In the Fastest Mixing Markov Chain problem, we are given a graph $G = (V, E)$ and desire the discrete-time Markov chain with smallest mixing time $\tau$ subject to having equilibrium distribution uniform on $V$ and non-zero transition…

This paper gathers together different conditions which are all equivalent to geometric ergodicity of time-homogeneous Markov chains on general state spaces. A total of 34 different conditions are presented (27 for general chains plus 7 just…

In this paper, it is presented a methodology for implementing arbitrarily constructed time-homogenous Markov chains with biochemical systems. Not only discrete but also continuous-time Markov chains are allowed to be computed. By employing…

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,…

Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…

The purpose of this paper is to study the time average behavior of Markov chains with transition probabilities being kernels of completely continuous operators, and therefore to provide a sufficient condition for a class of Markov chains…

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…

Let X_{n} be an integer valued Markov Chain with finite state space. Let S_{n}=\sum_{k=0}^{n}X_{k} and let L_{n}(x) be the number of times S_{k} hits x up to step n. Define the normalized local time process t_{n}(x) by…

Directed contact networks (DCNs) are a particularly flexible and convenient class of temporal networks, useful for modeling and analyzing the transfer of discrete quantities in communications, transportation, epidemiology, etc. Transfers…

Let $G$ be a finite tree with root $r$ and associate to the internal vertices of $G$ a collection of transition probabilities for a simple nondegenerate Markov chain. Embedd $G$ into a graph $G^\prime$ constructed by gluing finite linear…

In this paper we show that we can use Markov kernels as a model for optimal transport. This new framework can be easily translated into the standard coupling formulation of optimal transport, and we show that we can use a coupling as a…

For a discrete-time Markov chain $\{X(t)\}$ evolving on $\Re^\ell$ with transition kernel $P$, natural, general conditions are developed under which the following are established: 1. The transition kernel $P$ has a purely discrete spectrum,…

Convergence rates of Markov chains have been widely studied in recent years. In particular, quantitative bounds on convergence rates have been studied in various forms by Meyn and Tweedie [Ann. Appl. Probab. 4 (1994) 981-1101], Rosenthal…

We develop an approach to time-consistent risk evaluation of continuous-time processes in Markov systems. Our analysis is based on dual representation of coherent risk measures, differentiability concepts for multivalued mappings, and a…

In a series of previous works (arXiv:2104.11204, arXiv:2110.04565, arXiv:2301.07063), we gave a rigorous derivation of the homogeneous wave kinetic equation (WKE) up to small multiples of the kinetic timescale, which corresponds to short…

Convergence properties of time inhomogeneous Markov chain based discrete and continuous time linear consensus algorithms are analyzed. Provided that a so-called infinite jet flow property is satisfied by the underlying chains, necessary…

Let $X$ be a finite set and let $G$ be a finite group acting on $X$. The group action splits $X$ into disjoint orbits. The Burnside process is a Markov chain on $X$ which has a uniform stationary distribution when the chain is lumped to…

We explore the mathematical theory to rigorously describe the response of media with linear time-varying, generally dispersive, electromagnetic constitutive parameters. We show that even when the temporal inhomogeneity takes place on a time…

In the paper, we study a new rate of convergence estimate for homogeneous discrete-time nonlinear Markov chains based on the Markov-Dobrushin condition. This result generalizes the convergence estimates for any positive number of transition…

This paper is a survey of various proofs of the so called {\em fundamental theorem of Markov chains}: every ergodic Markov chain has a unique positive stationary distribution and the chain attains this distribution in the limit independent…