The central limit theorem for Markov chains with general state space

S. V. Nagaev

Matematičeskie trudy, Tome 21 (2018) no. 1, pp. 73-124.

Résumé

We consider a Markov chain with general state space and an embedded Markov chain sampled at the times of successive returns to a subset $A_0$ of the state space. We assume that the latter chain is uniformly ergodic but the original Markov chain need not possess this property. We develop a modification of the spectral method and utilize it in proving the central limit theorem for the Markov chain under consideration.

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