Geodesic
The spectral method and the central limit theorem for general Markov chains
Izvestiya. Mathematics , Tome 81 (2017) no. 6, pp. 1168-1211

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IM2_2017_81_6_a6,
     author = {S. V. Nagaev},
     title = {The spectral method and the central limit theorem for general {Markov} chains},
     journal = {Izvestiya. Mathematics },
     pages = {1168--1211},
     publisher = {mathdoc},
     volume = {81},
     number = {6},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2017_81_6_a6/}
}
TY  - JOUR
AU  - S. V. Nagaev
TI  - The spectral method and the central limit theorem for general Markov chains
JO  - Izvestiya. Mathematics 
PY  - 2017
SP  - 1168
EP  - 1211
VL  - 81
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2017_81_6_a6/
LA  - en
ID  - IM2_2017_81_6_a6
ER  - 
%0 Journal Article
%A S. V. Nagaev
%T The spectral method and the central limit theorem for general Markov chains
%J Izvestiya. Mathematics 
%D 2017
%P 1168-1211
%V 81
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2017_81_6_a6/
%G en
%F IM2_2017_81_6_a6
S. V. Nagaev. The spectral method and the central limit theorem for general Markov chains. Izvestiya. Mathematics , Tome 81 (2017) no. 6, pp. 1168-1211. http://geodesic.mathdoc.fr/item/IM2_2017_81_6_a6/