Bernstein type's concentration inequalities for symmetric Markov processes

Fuqing Gao; Arnaud Guillin; Liming Wu

Bernstein type's concentration inequalities for symmetric Markov processes

Probability 2010-02-11 v2

Authors: Fuqing Gao , Arnaud Guillin , Liming Wu

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.

Keywords

markov processes inequalities poisson processes

Cite

@article{arxiv.1002.2163,
  title  = {Bernstein type's concentration inequalities for symmetric Markov processes},
  author = {Fuqing Gao and Arnaud Guillin and Liming Wu},
  journal= {arXiv preprint arXiv:1002.2163},
  year   = {2010}
}

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