Related papers: Ergodic Theorems for discrete Markov chains

Let $G$ be a real connected algebraic semi-simple Lie group, and $H$ an algebraic subgroup of $G$. Let $\mu$ be a probability measure on $G$, with finite exponential moment, whose support spans a Zariski-dense subsemigroup of $G$. Let…

The aim of this paper is to propose a methodology for testing general hypothesis in a Markovian setting with random sampling. A discrete Markov chain X is observed at random time intervals $\tau$ k, assumed to be iid with unknown…

We justify and discuss expressions for joint lower and upper expectations in imprecise probability trees, in terms of the sub- and supermartingales that can be associated with such trees. These imprecise probability trees can be seen as…

We consider Markov chain with spectral gap in $L^2$ space. Assume that $f$ is a bounded function. Then the probabilities of large deviations of average along trajectory satisfy Hoeffding's-type inequalities. These bounds depend only on the…

We study the rate of convergence of the Markov chain on $S_n$ which starts with a random $(n-k)$-cycle for a fixed $k \geq 1$, followed by random transpositions. The convergence to the stationary distribution turns out to be of order $n$.…

In the present paper we show that for any given digraph $\mathbb{G} =([n], \vec{E})$, i.e. an oriented graph without self-loops and 2-cycles, one can construct a 1-dependent Markov chain and $n$ identically distributed hitting times $T_1,…

We prove an ergodic theorem for Markov chains indexed by the Ulam-Harris-Neveu tree over large subsets with arbitrary shape under two assumptions: with high probability, two vertices in the large subset are far from each other and have…

Let $a_n$ be the random increasing sequence of natural numbers which takes each value independently with decreasing probability of order $n^{-\alpha}$, $0 < \alpha < 1/2$. We prove that, almost surely, for every measure-preserving system…

We obtain non-Gaussian limit laws for one-dimensional random walk in a random environment assuming that the environment is a function of a stationary Markov process. This is an extension of the work of Kesten, M. Kozlov and Spitzer for…

Consider a compact metric space $S$ and a pair $(j,k)$ with $k \ge 2$ and $1 \le j \le k$. For any probability distribution $\theta \in P(S)$, define a Markov chain on $S$ by: from state $s$, take $k$ i.i.d. ($\theta$) samples, and jump to…

We consider a class of discrete time Markov chains with state space [0,1] and the following dynamics. At each time step, first the direction of the next transition is chosen at random with probability depending on the current location. Then…

We propose a random adaptation variant of time-varying distributed averaging dynamics in discrete time. We show that this leads to novel interpretations of fundamental concepts in distributed averaging, opinion dynamics, and distributed…

Markov chains can be used to generate samples whose distribution approximates a given target distribution. The quality of the samples of such Markov chains can be measured by the discrepancy between the empirical distribution of the samples…

We study a limit behavior of a sequence of Markov processes (or Markov chains) such that their distributions outside of any neighborhood of a "singular" point attract to some probability law. In any neighborhood of this point the behavior…

Rowmotion is a certain well-studied bijective operator on the distributive lattice $J(P)$ of order ideals of a finite poset $P$. We introduce the rowmotion Markov chain ${\bf M}_{J(P)}$ by assigning a probability $p_x$ to each $x\in P$ and…

We build optimal exponential bounds for the probabilities of large deviations of sums \sum_{k=1}^nf(X_k) where (X_k) is a finite reversible Markov chain and f is an arbitrary bounded function. These bounds depend only on the stationary mean…

Motivated by a derandomization of Markov chain Monte Carlo (MCMC), this paper investigates deterministic random walks, which is a deterministic process analogous to a random walk. While there are several progresses on the analysis of the…

Let $X$ be the constrained random walk on ${\mathbb Z}_+^2$ having increments $(1,0)$, $(-1,1)$, $(0,-1)$ with jump probabilities $\lambda(M_k)$, $\mu_1(M_k)$, and $\mu_2(M_k)$ where $M$ is an irreducible aperiodic finite state Markov…

We consider symmetric Markov chains on $\Bbb Z^d$ where we do {\bf not} assume that the conductance between two points must be zero if the points are far apart. Under a uniform second moment condition on the conductances, we obtain upper…

We obtain asymptotic expansions for probabilities $\mathbb{P}(S_N=k)$ of partial sums of uniformly bounded integer-valued functionals $S_N=\sum_{n=1}^N f_n(X_n)$ of uniformly elliptic inhomogeneous Markov chains. The expansions involve…