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The central limit theorem for Markov chains with normal transition operators, started at a point. (English) Zbl 0974.60017

Summary: 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.

MSC:

60F05 Central limit and other weak theorems
60J05 Discrete-time Markov processes on general state spaces
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