Estimate for $P_tD$ for the stochastic Burgers equation

Giuseppe Da Prato; Arnaud Debussche

Estimate for $P_tD$ for the stochastic Burgers equation

Probability 2014-12-24 v1

Authors: Giuseppe Da Prato , Arnaud Debussche

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.

Keywords

stochastic burgers equation transition semigroup invariant measure fomin differentiability integration by parts white noise malliavin calculus

Cite

@article{arxiv.1412.7426,
  title  = {Estimate for $P_tD$ for the stochastic Burgers equation},
  author = {Giuseppe Da Prato and Arnaud Debussche},
  journal= {arXiv preprint arXiv:1412.7426},
  year   = {2014}
}

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