The Markov approximation of the sequences of N-valued random variables and a class of small deviation theorems

Wen Liu and Weiguo Yang

Stochastic Processes and their Applications, 2000, vol. 89, issue 1, 117-130

Abstract: Let {Xn, n[greater-or-equal, slanted]0} be a sequence of random variables on the probability space ([Omega],F,P) taking values in the alphabet S={1,2,...,N}, and Q be another probability measure on F, under which {Xn, n[greater-or-equal, slanted]0} is a Markov chain. Let h(P Q) be the sample divergence rate of P with respect to Q related to {Xn}. In this paper the Markov approximation of {Xn, n[greater-or-equal, slanted]0} under P is discussed by using the notion of h(P Q), and a class of small deviation theorems for the averages of the bivariate functions of {Xn, n[greater-or-equal, slanted]0} are obtained. In the proof an analytic technique in the study of a.e. convergence together with the martingale convergence theorem is applied.

Keywords: Small; deviation; theorem; Entropy; Entropy; density; Sample; divergence; rate; Shannon-McMillan; theorem (search for similar items in EconPapers)
Date: 2000
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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