文章基本信息

标题：New Bernstein and Hoeffding type inequalities for regenerative Markov chains
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作者：Patrice Bertail ; Gabriela Ciołek
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2019
卷号：XVI
期号：1
页码：259-277
DOI：10.30757/ALEA.v16-09
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：The purpose of this paper is to present Bernstein and Hoeding type inequalitiesfor regenerative Markov chains. Furthermore, we generalize these resultsand establish exponential bounds for suprema of empirical processes over a class offunctions F which size is controlled by its uniform entropy number. All constantsinvolved in the bounds of the considered inequalities are given in an explicit formwhich can be advantageous for practical considerations. We present the theory forregenerative Markov chains, however the inequalities are also valid in the Harrisrecurrent case.
关键词：uniform entropy; exponential inequalities; empirical processes indexed;by classes of functions; regenerative Markov chain;