STATE-DEPENDENT CRITERIA FOR CONVERGENCE OF MARKOV CHAINS
成果类型：
Article
署名作者：
Meyn, Sean P.; Tweedie, R. L.
署名单位：
University of Illinois System; University of Illinois Urbana-Champaign; Colorado State University System; Colorado State University Fort Collins
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/aoap/1177005204
发表日期：
1994
页码：
149-168
关键词：
摘要：
The standard Foster-Lyapunov approach to establishing recurrence and ergodicity of Markov chains requires that the one-step mean drift of the chain be negative outside some appropriately finite set. Malyshev and Men'sikov developed a refinement of this approach for countable state space chains, allowing the drift to be negative after a number of steps depending on the starting state. We show that these countable space results are special cases of those in the wider context of phi-irreducible chains, and we give sample-path proofs natural for such chains which are rather more transparent than the original proofs of Malyshev and Men'sikov. We also develop an associated random-step approach giving similar conclusions. We further find state-dependent drift conditions sufficient to show that the chain is actually geometrically ergodic; that is, it has n-step transition probabilities which converge to their limits geometrically quickly. We apply these methods to a model of antibody activity and to a nonlinear threshold autoregressive model; they are also applicable to the analysis of complex queueing models.