Bounds on regeneration times and limit theorems for subgeometric Markov chains
Annales de l'I.H.P. Probabilités et statistiques, Tome 44 (2008) no. 2, p. 239-257
Nous établissons dans ce papier des théorèmes limites pour des chaînes de Markov à espace d'état général sous des conditions impliquant l'ergodicité sous géométrique. Sous des conditions de dérive et de minorisation plus faibles que celles de Foster-Lyapounov, nous obtenons un théorème de limite centrale et un principe de déviation modérée pour des fonctionnelles additives non nécessairement bornées de la chaîne de Markov. La preuve repose sur la méthode de régénération et un contrôle précis du moment modulé de temps d'atteinte d'ensembles petits.
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.
@article{AIHPB_2008__44_2_239_0,
     author = {Douc, Randal and Guillin, Arnaud and Moulines, \'Eric},
     title = {Bounds on regeneration times and limit theorems for subgeometric Markov chains},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {44},
     number = {2},
     year = {2008},
     pages = {239-257},
     doi = {10.1214/07-AIHP109},
     zbl = {1176.60063},
     mrnumber = {2446322},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2008__44_2_239_0}
}
Douc, Randal; Guillin, Arnaud; Moulines, Eric. Bounds on regeneration times and limit theorems for subgeometric Markov chains. Annales de l'I.H.P. Probabilités et statistiques, Tome 44 (2008) no. 2, pp. 239-257. doi : 10.1214/07-AIHP109. http://www.numdam.org/item/AIHPB_2008__44_2_239_0/

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