# Bernstein type's concentration inequalities for symmetric Markov processes

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 :
Document type :
Preprints, Working Papers, ...
Domain :

Cited literature [54 references]

https://hal.archives-ouvertes.fr/hal-00455598
Contributor : Arnaud Guillin <>
Submitted on : Thursday, February 11, 2010 - 8:54:37 PM
Last modification on : Thursday, March 7, 2019 - 2:04:15 PM
Long-term archiving on : Thursday, September 23, 2010 - 11:29:54 AM

### Files

Bernstein-ggw.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-00455598, version 2
• ARXIV : 1002.2163

### Citation

Fuqing Gao, Arnaud Guillin, Liming Wu. Bernstein type's concentration inequalities for symmetric Markov processes. 2010. ⟨hal-00455598v2⟩

Record views