Renewal theory for functionals of a Markov chain with compact state space

• 成果类型: Article
• 署名作者: Klüppelberg, C; Pergamenchtchikov, S
• 署名单位: Technical University of Munich; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2003
• 页码: 2270-2300
• 关键词: stochastic difference equation

摘要

Motivated by multivariate random recurrence equations we prove a new analogue of the Key Renewal Theorem for functionals of a Markov chain with compact state space in the spirit of Kesten [Ann. Probab. 2 (1974) 355-386]. Compactness of the state space and a certain continuity condition allows us to simplify Kesten's proof considerably.