Bernstein type's concentration inequalities for symmetric Markov processes

Fuqing Gao; Arnaud Guillin; Liming Wu

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arXiv · 1002.2163

Bernstein type's concentration inequalities for symmetric Markov processes

Fuqing Gao·Arnaud Guillin·Liming Wu

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Abstract

Using the method of transportation-information inequality introduced in \cite{GLWY}, we establish Bernstein type's concentration inequalities for empirical means $\frac 1t \int_0^t g(X_s)ds$ 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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Fuqing Gao, Arnaud Guillin, Liming Wu. 2010-02-11. Bernstein type's concentration inequalities for symmetric Markov processes. https://arxiv.org/abs/1002.2163

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