Deviation bounds for additive functionals of Markov process

الأصل · EN

In this paper we derive non asymptotic deviation bounds for ¶ν(| 1t ∫₀ᵗ V(Xₛ) ds - ∫ V dμ| ≥ 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...).