Bernstein type's concentration inequalities for symmetric Markov processes

2010/02/10 by Gao, Fuqing, Guillin, Arnaud, Wu, Liming · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1002.2163

Abstract

Using the method of transportation-information inequality introduced in \citeGLWY, we establish Bernstein type's concentration inequalities for empirical means \frac 1t ∫₀^t g(X_s)ds where g is a unbounded observable of the symmetric Markov process (X_t). Three approaches are proposed : functional inequalities approach ; Lyapunov function method ; and an approach through the Lipschitzian norm of the solution to the Poisson equation. Several applications and examples are studied.

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• Exact rate of convergence for the empirical measure of a subordinated process in p-Wasserstein distance

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