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April 2000 Central limit theorems for additive functionals of Markov chains
Michael Maxwell, Michael Woodroofe
Ann. Probab. 28(2): 713-724 (April 2000). DOI: 10.1214/aop/1019160258

Abstract

Central limit theorems and invariance principles are obtained for additive functionals of a stationary ergodic Markov chain, say $S_n = g(X_1)+ \cdots + g(X_n)$ where $E[g(X_1)]= 0$ and $E[g(X_1)^2]<\infty$. The conditions imposed restrict the moments of $g$ and the growth of the conditional means $E(S_n|X_1)$. No other restrictions on the dependence structure of the chain are required. When specialized to shift processes,the conditions are implied by simple integral tests involving $g$.

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Michael Maxwell. Michael Woodroofe. "Central limit theorems for additive functionals of Markov chains." Ann. Probab. 28 (2) 713 - 724, April 2000. https://doi.org/10.1214/aop/1019160258

Information

Published: April 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1044.60014
MathSciNet: MR1782272
Digital Object Identifier: 10.1214/aop/1019160258

Subjects:
Primary: 60F05

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 2 • April 2000
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