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additive functionals.

ESAIM: Probability and Statistics (1)

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deviation bounds for additive functionals of markov processes
Patrick Cattiaux, Arnaud Guillin
Journal:

ESAIM: Probability and Statistics / Volume 12 / 2008

Published online by Cambridge University Press:

13 November 2007, pp. 12-29

Print publication:

2008
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In this paper we derive non asymptotic deviation bounds for $${\mathbb P}_\nu (|\frac 1t\int_0^t V(X_s) {\rm d}s - \int V {\rm d} \mu | \geq R)$$ where X is a μ stationary and ergodic Markov process and V is some μ integrable function. These bounds are obtained under various moments assumptions for V, and various regularity assumptions for μ. Regularity means here that μ may satisfy various functional inequalities (F-Sobolev,generalized Poincaré etc.).