Sharp bounds for the tails of functionals of Markov chains

P. Bertail; S. Clémençon

doi:10.1137/S0040585X97984401

Sharp bounds for the tails of functionals of Markov chains

P. Bertail
, S. Clémençon

Université Paris-Nanterre

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

18 Citations (Scopus)

Résumé

This paper is devoted to establishing sharp bounds for deviation probabilities of partial sums Σⁿ_i=1 f(X _i), where X = (X_n)_n∈N is a positive recurrent Markov chain and f is a real valued function defined on its state space. Combining the regenerative method to the Esscher transformation, these estimates are shown in particular to generalize probability inequalities proved in the independent i.i.d. case to the Markovian setting for (not necessarily uniformly) geometrically ergodic chains.

langue originale	Anglais
Pages (de - à)	505-515
Nombre de pages	11
journal	Theory of Probability and its Applications
Volume	54
Numéro de publication	3
Les DOIs	https://doi.org/10.1137/S0040585X97984401
état	Publié - 29 nov. 2010

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10.1137/S0040585X97984401

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KW - Regenerative method

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Sharp bounds for the tails of functionals of Markov chains

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