Related papers: Coupling Markov chains with a common image chain
We consider a Markov chain of point processes such that each state is a super position of an independent cluster process with the previous state as its centre process together with some independent noise process. The model extends earlier…
Dealing with finite Markov chains in discrete time, the focus often lies on convergence behavior and one tries to make different copies of the chain meet as fast as possible and then stick together. There is, however, a very peculiar kind…
Necessary and sufficient conditions for identifying strong lumpability in Markov chains are presented. We show that the states in a lump necessarily correspond to identical elements in eigenvectors of the dual transition matrix. If there…
The correspondence between weighted undirected graphs and reversible Markov chains via vertex random walks is simple and well known. Leveraging this correspondence and ideas from the theory of dynamical systems, we study the structural…
Let $\{W_t\}_{t=1}^{\infty}$ be a finite state stationary Markov chain, and suppose that $f$ is a real-valued function on the state space. If $f$ is bounded, then Gillman's expander Chernoff bound (1993) provides concentration estimates for…
We provide a general framework for computing upper bounds on mixing times of finite Markov chains when its minimal ideal is left zero. Our analysis is based on combining results by Brown and Diaconis with our previous work on stationary…
It is well-known that discrete-time finite-state Markov Chains, which are described by one-sided conditional probabilities which describe a dependence on the past as only dependent on the present, can also be described as one-dimensional…
Classical graphical modeling of multivariate random vectors uses graphs to encode conditional independence. In graphical modeling of multivariate stochastic processes, graphs may encode so-called local independence analogously. If some…
We consider finite-state time-nonhomogeneous Markov chains where the probability of moving from state $i$ to state $j\neq i$ at time $n$ is $G(i,j)/n^\zeta$ for a ``generator'' matrix $G$ and strength parameter $\zeta>0$. In these chains,…
The hitting and mixing times are two fundamental quantities associated with Markov chains. In Peres and Sousi[PS2015] and Oliveira[Oli2012], the authors show that the mixing times and "worst-case" hitting times of reversible Markov chains…
Synchronization of fractional-order chaotic systems is a hot topic in the field of nonlinear study. The co-coupled synchronization between two fractional-order chaotic systems with different initial conditions is investigated in this paper.…
In this article we extend the coupling method from classical probability theory to quantum Markov chains on atomic von Neumann algebras. In particular, we establish a coupling inequality, which allow us to estimate convergence rates by…
This is an expository paper, focussing on the following scenario. We have two Markov chains, $\mathcal {M}$ and $\mathcal {M}'$. By some means, we have obtained a bound on the mixing time of $\mathcal {M}'$. We wish to compare $\mathcal…
We study the ergodic behaviour of a discrete-time process $X$ which is a Markov chain in a stationary random environment. The laws of $X_t$ are shown to converge to a limiting law in (weighted) total variation distance as $t\to\infty$.…
We derive two sufficient conditions for a function of a Markov random field (MRF) on a given graph to be a MRF on the same graph. The first condition is information-theoretic and parallels a recent information-theoretic characterization of…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
We study a class of matrices with a rank-1 interconnection structure, and derive a simple necessary and sufficient condition for diagonal stability. The underlying Lyapunov function is used to provide sufficient conditions for diagonal…
In this short note we provide an elementary proof that a certain type of nonuniform sequential Doeblin minorization condition implies non-uniform sequential "geometric" ergodicity. Using this result several limit theorems for inhomogeneous…
Markov chains are convenient means of generating realizations of networks with a given (joint or otherwise) degree distribution, since they simply require a procedure for rewiring edges. The major challenge is to find the right number of…
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…