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The central limit theorem for Markov chains with normal transition operators, started at a point
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  • Published: April 2001

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

  • Yves Derriennic1 &
  • Michael Lin2 

Probability Theory and Related Fields volume 119, pages 508–528 (2001)Cite this article

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  • 44 Citations

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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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Authors and Affiliations

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

    Yves Derriennic

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

    Michael Lin

Authors
  1. Yves Derriennic
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  2. Michael Lin
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Received: 28 March 2000 / Revised version: 25 July 2000 /¶Published online: 15 February 2001

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Derriennic, Y., Lin, M. The central limit theorem for Markov chains with normal transition operators, started at a point. Probab Theory Relat Fields 119, 508–528 (2001). https://doi.org/10.1007/PL00008769

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  • Issue Date: April 2001

  • DOI: https://doi.org/10.1007/PL00008769

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