Invariance principles with logarithmic averaging for Markov processes

• 成果类型: Article
• 署名作者: Maaoula, F
• 署名单位: Universite de Tunis-El-Manar; Faculte des Sciences de Tunis (FST)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1015345775
• 发表日期: 2001
• 页码: 1859-1902
• 关键词: CENTRAL-LIMIT-THEOREM; random-variables; iterated logarithm; STABILITY; chains; LAW

摘要

We extend the almost-sure central limit theorem to martingale additive functionals of a recurrent Markov process. In the particular case of positive recurrence, we also derive two invariance principles similar to the central limit theorem and the law of the iterated logarithm.