Absolute regularity and functions of Markov chains

Richard C. Bradley

Stochastic Processes and their Applications, 1983, vol. 14, issue 1, 67-77

Abstract: We first give an extension of a theorem of Volkonskii and Rozanov characterizing the strictly stationary random sequences satisfying 'absolute regularity'. Then a strictly stationary sequence {Xk, K = ..., -1, 0, 1,...} is constructed which is a 0-1 instantaneous function of an aperiodic Markov chain with countable irreducible state space, such that n-2 var (X1 + ... + Xn) approaches 0 arbitrarily slowly as n --> [infinity] and (X1 + ... + Xn) is partially attracted to every infinitely divisible law.

Keywords: Absolute; regularity; central; limit; theorem; infinitely; divisible; law; weak; Bernoulli; mixing; Markov; chain (search for similar items in EconPapers)
Date: 1983
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