Asymptotic properties of a singularly perturbed Markov chain with inclusion of transient states

• 成果类型: Article
• 署名作者: Yin, G; Zhang, Q; Badowski, G
• 署名单位: Wayne State University; University System of Georgia; University of Georgia
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2000
• 页码: 549-572
• 关键词: weak

摘要

This work is concerned with aggregations in a singularly perturbed Markov chain having a finite state space and fast and slow motions. The state space of the underlying Markov chain can be decomposed into several groups of recurrent states and a group of transient states. The asymptotic properties are studied through sequences of unscaled and scaled occupation measures. By treating the states within each recurrent class as a single state, an aggregated process is defined and shown to be convergent to a limit Markov chain. In addition, it is shown that a sequence of suitably rescaled occupation measures converges to a switching diffusion process weakly.