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On the limit laws of the second order for additive functionals of Harris recurrent Markov chains
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  • Published: January 2000

On the limit laws of the second order for additive functionals of Harris recurrent Markov chains

  • Xia Chen1 

Probability Theory and Related Fields volume 116, pages 89–123 (2000)Cite this article

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  • 12 Citations

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Abstract.

Let {X n } n ≥0 be a Harris recurrent Markov chain with state space E and invariant measure π. The law of the iterated logarithm and the law of weak convergence are given for the additive functionals of the form

where ƒ is a real π-centered function defined on E. Some similar results are also obtained for additive functionals which are martingales associated with {X n } n ≥0.

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Authors and Affiliations

  1. Xia Chen Department of Mathematics, University of Utah, Salt Lake City, UT 84112 USA. e-mail: xchen@math.utah.edu, , , , , , US

    Xia Chen

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  1. Xia Chen
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Received: 15 September 1998 / Revised version: 1 April 1999

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Chen, X. On the limit laws of the second order for additive functionals of Harris recurrent Markov chains. Probab Theory Relat Fields 116, 89–123 (2000). https://doi.org/10.1007/PL00008724

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  • Issue Date: January 2000

  • DOI: https://doi.org/10.1007/PL00008724

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  • Key words and phrases: Law of the iterated logarithm – Weak convergence – Harris recurrence – Regularity
  • Mathematics Subject Classification (1991): 60F10, 60J10
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