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