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Article Dans Une Revue Theory of Probability and Its Applications c/c of Teoriia Veroiatnostei i Ee Primenenie Année : 2013

Bernstein type's concentration inequalities for symmetric Markov processes

Résumé

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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Dates et versions

hal-00455598 , version 1 (10-02-2010)
hal-00455598 , version 2 (11-02-2010)

Identifiants

Citer

Fuqing Gao, Arnaud Guillin, Liming Wu. Bernstein type's concentration inequalities for symmetric Markov processes. Theory of Probability and Its Applications c/c of Teoriia Veroiatnostei i Ee Primenenie, 2013, 58 (3), pp.521-549. ⟨10.4213/tvp4524⟩. ⟨hal-00455598v2⟩
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