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Deviation bounds for additive functionals of Markov process

Patrick Cattiaux·Arnaud Guillin
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Abstract

In this paper we derive non asymptotic deviation bounds for $$¶_ν(|\frac 1t \int_0^t V(X_s) ds - \int V dμ| \geq R)$$ 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...).

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Patrick Cattiaux, Arnaud Guillin. 2006-03-01. Deviation bounds for additive functionals of Markov process. https://arxiv.org/abs/math/0603021

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