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On variance conditions for Markov chain CLTs. (English) Zbl 1191.60082

Summary: Central limit theorems (CLT) for Markov chains are considered, and in particular the relationships between various expressions for asymptotic variance known from the literature. These turn out to be equal under fairly general conditions, although not always. We also investigate the existence of CLTs, and pose some open problems.

MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60F05 Central limit and other weak theorems