ERGODICITY OF INHOMOGENEOUS MARKOV CHAINS THROUGH ASYMPTOTIC PSEUDOTRAJECTORIES

• 成果类型: Article
• 署名作者: Benaim, Michel; Bouguet, Florian; Cloez, Bertrand
• 署名单位: University of Neuchatel; Universite de Lorraine; INRAE; Institut Agro; Montpellier SupAgro; Universite de Montpellier; Universite de Lorraine; Universite de Lorraine; INRAE; Institut Agro; Montpellier SupAgro
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/17-AAP1275
• 发表日期: 2017
• 页码: 3004-3049
• 关键词: stochastic-approximation; CONVERGENCE; EQUATIONS; DYNAMICS; THEOREM; models; rates

摘要

In this work, we consider an inhomogeneous (discrete time) Markov chain and are interested in its long time behavior. We provide sufficient conditions to ensure that some of its asymptotic properties can be related to the ones of a homogeneous (continuous time) Markov process. Renowned examples such as a bandit algorithms, weighted random walks or decreasing step Euler schemes are included in our framework. Our results are related to functional limit theorems, but the approach differs from the standard Tightness/Identification argument; our method is unified and based on the notion of pseudotrajectories on the space of probability measures.