Siberian Advances in Mathematics

, Volume 28, Issue 4, pp 265–302 | Cite as

The Central Limit Theorem for Markov Chains with General State Space

  • S. V. NagaevEmail author


We consider a Markov chain with general state space and an embedded Markov chain sampled at the times of successive returns to a subsetA0 of the state space.We assume that the latter chain is uniformly ergodic but the originalMarkov chain need not possess this property.We develop amodification of the spectralmethod and utilize it in proving the central limit theorem for theMarkov chain under consideration.


central limit theorem Markov chain transition function space of complex-valued measures spectral method resolvent kernel of an operator 


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© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia

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