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Izv. RAN. Ser. Mat., 2017, Volume 81, Issue 6, Pages 114–157 (Mi izv8537)  

The spectral method and the central limit theorem for general Markov chains

S. V. Nagaev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: We consider Markov chains with an arbitrary phase space and develop a modification of the spectral method that enables us to prove the central limit theorem (CLT) for non-uniformly ergodic Markov chains. The conditions imposed on the transition function are more general than those by Athreya–Ney and Nummelin. Our proof of the CLT is purely analytical.

Keywords: transition function, space of complex measures, spectral method, resolvent, kernel of an operator.

DOI: https://doi.org/10.4213/im8537

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English version:
Izvestiya: Mathematics, 2017, 81:6, 1168–1211

Bibliographic databases:

UDC: 519.21+517.98
MSC: 60J10, 47A35
Received: 02.03.2016
Revised: 17.08.2016

Citation: S. V. Nagaev, “The spectral method and the central limit theorem for general Markov chains”, Izv. RAN. Ser. Mat., 81:6 (2017), 114–157; Izv. Math., 81:6 (2017), 1168–1211

Citation in format AMSBIB
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  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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