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.
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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

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

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

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