A deviation inequality for non-reversible Markov processes

doi:10.1016/S0246-0203(00)00135-7

Annales de l'Institut Henri Poincare (B) Probability and Statistics

Volume 36, Issue 4, July 2000, Pages 435-445

https://doi.org/10.1016/S0246-0203(00)00135-7 Get rights and content

Abstract

Using the dissipative criterion of Lumer–Philips for the contraction semigroup, we get in this Note a new deviation inequality for $∫ 0 t V(X_{s}) ds$ by means of the symmetrized Dirichlet form. A more explicit version is obtained in the case where the logarithmic Sobolev inequality holds.

Résumé

Par le critère de dissipativité de Lumer–Philips pour la contractivité de semigroupes, on obtient une inégalité nouvelle de déviation pour $∫ 0 t V(X_{s}) ds$ via la forme de Dirichlet symmetrisée. Une expression plus explicite est obtenue dans le cas où l'inégalité de Sobolev logarithmique est vraie.

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A deviation inequality for non-reversible Markov processes

Abstract

Résumé

J. Funct. Anal.

The rate function of hypoelliptic diffusions

Comm. Pure Appl. Math.

On the convergence of averages of mixing sequences

J. Theoret. Probab.

Martingale representation and a simple proof of logarithmic Sobolev inequality on path spaces

Elect. Comm. Probab.