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The central limit theorem for stationary Markov chains under invariant splittings. (English) Zbl 1077.60023

The authors formulate a new sufficient condition for the central limit theorem (CLT) and give a short survey of related results on the CLT for general not necessarily Harris recurrent chains. Furthermore, Markov operators are considered which admit invariant orthogonal splittings of the space of square-integrable functions. The authors show how conditions for the CLT can be improved if this additional structure is taken into account. Finally they give examples of this situation, namely endomorphisms of compact Abelian groups and random walks on compact homogeneous spaces.

MSC:

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