文章基本信息

标题：Limit theorems for monotone Markov processes
本地全文：下载
作者：Rabi Bhattacharya The University of Arizona, Tucson ; USA Mukul Majumdar Cornell University, Ithaca ; USA Nigar Hashimzade University of Reading, Reading, UK 等
期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2010
卷号：72
期号：01
页码：170--190
出版社：Indian Statistical Institute
摘要：This article considers the convergence to steady states of Markov processes generated by the action of successive i.i.d. monotone maps on a subset S of an Eucledian space. Without requiring irreducibility or Harris recurrence, a ¡°splitting¡± condition guarantees the existence of a unique invariant probability as well as an exponential rate of convergence to it in an appropriate metric. For a special class of Harris recurrent processes on [0,∞) of interest in economics, environmental studies and queuing theory, criteria are derived for polynomial and exponential rates of convergence to equilibrium in total variation distance. Central limit theorems follow as consequences.
关键词：Markov processes, coupling, monotone i.i.d. maps, polynomial convergence rates.