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The central limit theorem for Markov chains started at a point
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  • Published: January 2003

The central limit theorem for Markov chains started at a point

  • Yves Derriennic1 &
  • Michael Lin2 

Probability Theory and Related Fields volume 125, pages 73–76 (2003)Cite this article

  • 371 Accesses

  • 43 Citations

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Abstract

 The aim of this paper is to prove a central limit theorem and an invariance principle for an additive functional of an ergodic Markov chain on a general state space, with respect to the law of the chain started at a point. No irreducibility assumption nor mixing conditions are imposed; the only assumption bears on the growth of the L 2-norms of the ergodic sums for the function generating the additive functional, which must be with . The result holds almost surely with respect to the invariant probability of the chain.

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Authors and Affiliations

  1. Département de Mathématiques, Université de Bretagne Occidentale 6 Avenue Le Gorgeu, 29285 Brest, France. e-mail: derrienn@univ-brest.fr, , , , , , FR

    Yves Derriennic

  2. Department of Mathematics, Ben-Gurion University of the Negev Beer-Sheva, Israel. e-mail: lin@bgu.ac.il, , , , , , IL

    Michael Lin

Authors
  1. Yves Derriennic
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  2. Michael Lin
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Additional information

Received: 17 October 2001 / Revised version: 5 April 2002 / Published Online: 24 October 2002

Mathematics Subject Classification (2000): 60F05, 60J05

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Derriennic, Y., Lin, M. The central limit theorem for Markov chains started at a point. Probab Theory Relat Fields 125, 73–76 (2003). https://doi.org/10.1007/s004400200215

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  • Issue Date: January 2003

  • DOI: https://doi.org/10.1007/s004400200215

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Keywords

  • Markov Chain
  • Limit Theorem
  • Central Limit
  • Central Limit Theorem
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