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Journal Articles Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Year : 2016

Estimate for $P_tD$ for the stochastic Burgers equation

Abstract

We consider the Burgers equation on $H=L^2(0,1)$ perturbed by white noise and the corresponding transition semigroup $P_t$. We prove a new formula for $P_tD\varphi$ (where $\varphi:H\to\R$ is bounded and Borel) which depends on $\varphi$ but not on its derivative. Then we deduce some new consequences for the invariant measure $\nu$ of $P_t$ as its Fomin differentiability and an integration by parts formula which generalises the classical one for gaussian measures.

Dates and versions

hal-01110454 , version 1 (28-01-2015)

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Giuseppe da Prato, Arnaud Debussche. Estimate for $P_tD$ for the stochastic Burgers equation. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2016, 52 (3), pp.1248-1258. ⟨10.1214/15-AIHP685⟩. ⟨hal-01110454⟩
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