Deviation bounds for additive functionals of Markov process

Abstract

In this paper we derive non asymptotic deviation bounds for $${\P }_{\nu }(|\frac{1}{t}{\int }_0^{t}V(X_s)ds-\int Vd\mu |\ge R)$$ where $X$ is a $\mu$ stationary and ergodic Markov process and $V$ is some $\mu$ integrable function. These bounds are obtained under various moments assumptions for $V$, and various regularity assumptions for $\mu$. Regularity means here that $\mu$ may satisfy various functional inequalities (F-Sobolev, generalized Poincaré etc...).

References in corpus (3)

• Transportation cost-information inequalities and applications to random dynamical systems and diffusions
• Isoperimetry between exponential and Gaussian
• Weak logarithmic Sobolev inequalities and entropic convergence

Cited by in corpus (5)

• A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature
• Transportation-information inequalities for Markov processes (II) : relations with other functional inequalities
• Trends to Equilibrium in Total Variation Distance
• Weak logarithmic Sobolev inequalities and entropic convergence
• Transportation-information inequalities for Markov processes