Related papers: Markovian embeddings of general random strings

The embedding problem for Markov chains is a famous problem in probability theory and only partial results are available up till now. In this paper, we propose a variant of the embedding problem called the reversible embedding problem which…

We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…

The asymptotic normality in multi-dimension of the nonparametric estimator of the transition probabilities of a Markov renewal chain is proved, and is applied to that of other nonparametric estimators involved with the associated…

In this paper, we examine the existence of the R\'enyi divergence between two time invariant general hidden Markov models with arbitrary positive initial distributions. By making use of a Markov chain representation of the probability…

Adaptive Markov chains are an important class of Monte Carlo methods for sampling from probability distributions. The time evolution of adaptive algorithms depends on past samples, and thus these algorithms are non-Markovian. Although there…

The partial sum of the states of a Markov chain or more generally a Markov source is asymptotically normally distributed under suitable conditions. One of these conditions is that the variance is unbounded. A simple combinatorial…

Markov chain Monte Carlo (MCMC) has transformed Bayesian model inference over the past three decades: mainly because of this, Bayesian inference is now a workhorse of applied scientists. Under general conditions, MCMC sampling converges…

Let {X_n,n\geq0} be a Markov chain on a general state space X with transition probability P and stationary probability \pi. Suppose an additive component S_n takes values in the real line R and is adjoined to the chain such that…

Let $(X_n)_{n \ge 0}$ be an irreducible, aperiodic, homogeneous Markov chain, with state space a totally ordered finite alphabet of size $m$. Using combinatorial constructions and weak invariance principles, we obtain the limiting shape of…

In order to approximate a continuous time stochastic process by discrete time Markov chains one has several options to embed the Markov chains into continuous time processes. On the one hand there is the Markov embedding, which uses…

The paper is concerned with approximating the distribution of a sum W of n integer valued random variables Y_i, whose distributions depend on the state of an underlying Markov chain X. The approximation is in terms of a translated Poisson…

We address the algorithmic problem of determining the reversible Markov chain $\tilde X$ that is closest to a given Markov chain $X$, with an identical stationary distribution. More specifically, $\tilde X$ is the reversible Markov chain…

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…

For any continuous zero-mean random variable (r.v.) X, a reciprocating function r is constructed, based only on the distribution of X, such that the conditional distribution of X given the (at-most-)two-point set {X,r(X)} is the zero-mean…

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…

We study the following model of hidden Markov chain: $Y_i=X_i+\epsilon_i$, $ i=1,...,n+1$ with $(X_i)$ a real-valued positive recurrent and stationary Markov chain and $(\epsilon_i)_{1\leq i\leq n+1}$ a noise independent of the sequence…

Iteration of randomly chosen quadratic maps defines a Markov process: X_{n+1}=\epsilon_{n+1}X_n(1-X_n), where \epsilon_n are i.i.d. with values in the parameter space [0,4] of quadratic maps F_{\theta}(x)=\theta x(1-x). Its study is of…

We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…

We present a comprehensive new framework for handling biologically accurate models of molecular evolution. This model provides a systematic framework for studying models of molecular evolution that implement heterogeneous rates,…

This article presents a review of some old and new results on the long time behavior of reflected diffusions. First, we present a summary of prior results on construction, ergodicity and geometric ergodicity of reflected diffusions in the…