相关论文: Exponential rate of convergence for some Markov op…

Markov decision processes continue to gain in popularity for modeling a wide range of applications ranging from analysis of supply chains and queuing networks to cognitive science and control of autonomous vehicles. Nonetheless, they tend…

A new approach is developed for evaluating the convergence rate for nonlinear Markov chains (MC) based on the recently developed spectral radius technique of markovian coupling for linear MC and the idea of small nonlinear perturbations of…

Finding the entropy rate of Hidden Markov Processes is an active research topic, of both theoretical and practical importance. A recently used approach is studying the asymptotic behavior of the entropy rate in various regimes. In this…

In this article we consider the Markovian products of invertible (not necessarily positive) matrices chosen from a strongly irreducible, contracting, finite set of matrices. We construct Markovian transfer operators and prove the spectral…

In this paper we recall some results and some criteria on the convergence of matrix continued fractions. The aim of this paper is to give some properties and results of continued fractions with matrix arguments. Then we give continued…

Polynomial convergence rate to stationarity is shown for extended Erlang -- Sevastyanov's model.

We study ergodic properties of a class of Markov-modulated general birth-death processes under fast regime switching. The first set of results concerns the ergodic properties of the properly scaled joint Markov process with a parameter that…

We consider additive functionals of Markov processes in continuous time with general (metric) state spaces. We derive concentration bounds for their exponential moments and moments of finite order. Applications include diffusions,…

We provide conditions that guarantee local rates of convergence in distribution of iterated random functions that are not nonexpansive mappings in locally compact Hadamard spaces. Our results are applied to stochastic instances of common…

Chernoff approximations to strongly continuous one-parameter semigroups give solutions to a wide class of differential equations. This paper studies the rate of convergence of the Chernoff approximations. We provide simple natural examples…

We investigate the performance and robustness of distributed averaging integral controllers used in the optimal frequency regulation of power networks. We construct a strict Lyapunov function that allows us to quantify the exponential…

In Monte-Carlo methods the Markov processes used to sample a given target distribution usually satisfy detailed balance, i.e. they are time-reversible. However, relatively recent results have demonstrated that appropriate reversible and…

In this article, we analyse the Kantorovich type exponential sampling operators and its linear combination. We derive the Voronovskaya type theorem and its quantitative estimates for these operators in terms of an appropriate K-functional.…

We are interested in the rate of convergence of a subordinate Markov process to its invariant measure. Given a subordinator and the corresponding Bernstein function (Laplace exponent) we characterize the convergence rate of the subordinate…

We prove exponential decay of pair correlations for 1D stationary point processes when spacings satisfy a Markov condition, geometric ergodicity, and a condition on exponential moments. The conditions are phrased for stationary sequences of…

The exponential upper bounds for the convergence rate of the distribution of restorable element with partially energized standby redundancy are founded, in the case when all working and repair times are bounded by exponential random…

We consider general Markov processes with absorption and provide criteria ensuring the exponential convergence in total variation of the distribution of the process conditioned not to be absorbed. The first one is based on two-sided…

We prove the convergence at an exponential rate towards the invariant probability measure for a class of solutions of stochastic differential equations with finite delay. This is done, in this non-Markovian setting, using the cluster…

In a recent paper, Melbourne and Terhesiu [Operator renewal theory and mixing rates for dynamical systems with infinite measure, Invent. Math. 189 (2012), 61-110] obtained results on mixing and mixing rates for a large class of…

Lecture notes (in French) of a master 2 level course in applied mathematics. Contents: Part I. Markov chains on a countable space. 1. Examples 2. Summary of basic properties. 3. Spectral theory and speed of convergence. 4. Lyapunov…