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

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	505-515
Number of pages	11
Journal	Theory of Probability and its Applications
Volume	54
Issue number	3
DOIs	https://doi.org/10.1137/S0040585X97984401
Publication status	Published - 29 Nov 2010

Keywords

Markov chain
Probability inequalities
Regenerative method

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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

Abstract

Keywords

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