Absolute regularity and functions of Markov chains |
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| Authors: | Richard C Bradley |
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| Institution: | Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A. |
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| 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 → ∞ and (X1 + ? + Xn) is partially attracted to every infinitely divisible law. |
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| Keywords: | Absolute regularity central limit theorem infinitely divisible law weak Bernoulli mixing Markov chain |
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