This paper studies limit theorems for Markov chains with general state space under conditions which imply subgeometric ergodicity. We obtain a central limit theorem and moderate deviation principles for additive not necessarily bounded functional of the Markov chains under drift and minorization conditions which are weaker than the Foster–Lyapunov conditions. The regeneration-split chain method and a precise control of the modulated moment of the hitting time to small sets are employed in the proof.
Publié le : 2008-04-15
Classification:
Stochastic monotonicity,
Rates of convergence,
Markov chains,
60J10
@article{1207948218,
author = {Douc, Randal and Guillin, Arnaud and Moulines, Eric},
title = {Bounds on regeneration times and limit theorems for subgeometric Markov chains},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {44},
number = {2},
year = {2008},
pages = { 239-257},
language = {en},
url = {http://dml.mathdoc.fr/item/1207948218}
}
Douc, Randal; Guillin, Arnaud; Moulines, Eric. Bounds on regeneration times and limit theorems for subgeometric Markov chains. Ann. Inst. H. Poincaré Probab. Statist., Tome 44 (2008) no. 2, pp. 239-257. http://gdmltest.u-ga.fr/item/1207948218/