The central limit theorem for Markov chains with normal transition operators, started at a point

Yves Derriennic; Michael Lin

doi:10.1007/PL00008769

The central limit theorem for Markov chains with normal transition operators, started at a point

Yves Derriennic, Michael Lin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

49 Scopus citations

Abstract

The central limit theorem and the invariance principle, proved by Kipnis and Varadhan for reversible stationary ergodic Markov chains with respect to the stationary law, are established with respect to the law of the chain started at a fixed point, almost surely, under a slight reinforcing of their spectral assumption. The result is valid also for stationary ergodic chains whose transition operator is normal.

Original language	English
Pages (from-to)	508-528
Number of pages	21
Journal	Probability Theory and Related Fields
Volume	119
Issue number	4
DOIs	https://doi.org/10.1007/PL00008769
State	Published - 1 Jan 2001

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/PL00008769

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title = "The central limit theorem for Markov chains with normal transition operators, started at a point",

abstract = "The central limit theorem and the invariance principle, proved by Kipnis and Varadhan for reversible stationary ergodic Markov chains with respect to the stationary law, are established with respect to the law of the chain started at a fixed point, almost surely, under a slight reinforcing of their spectral assumption. The result is valid also for stationary ergodic chains whose transition operator is normal.",

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N2 - The central limit theorem and the invariance principle, proved by Kipnis and Varadhan for reversible stationary ergodic Markov chains with respect to the stationary law, are established with respect to the law of the chain started at a fixed point, almost surely, under a slight reinforcing of their spectral assumption. The result is valid also for stationary ergodic chains whose transition operator is normal.

AB - The central limit theorem and the invariance principle, proved by Kipnis and Varadhan for reversible stationary ergodic Markov chains with respect to the stationary law, are established with respect to the law of the chain started at a fixed point, almost surely, under a slight reinforcing of their spectral assumption. The result is valid also for stationary ergodic chains whose transition operator is normal.

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The central limit theorem for Markov chains with normal transition operators, started at a point

Abstract

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