I-PROJECTION AND CONDITIONAL LIMIT-THEOREMS FOR DISCRETE PARAMETER MARKOV-PROCESSES

• 成果类型: Article
• 署名作者: SCHROEDER, C
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989265
• 发表日期: 1993
• 页码: 721-758
• 关键词: asymptotic evaluation; process expectations; large time

摘要

Let (X, B) be a compact metric space with B the sigma-field of Borel sets. Suppose this is the state space of a discrete parameter Markov process. Let C be a closed convex set of probability measures on X. Known results on the asymptotic behavior of the probability that the empirical distributions P(n) belong to C and new results on the Markov process distribution of omega0,..., omega(n-1) under the condition P(n) is-an-element-of C are obtained simultaneously through a large deviations estimate. In particular, the Markov process distribution under the condition P(n) is-an-element-of C is shown to have an asymptotic quasi-Markov property, generalizing a concept of Csiszar.