Estimate for P_tD for the stochastic Burgers equation

2014/12/23 by Giuseppe Da Prato, Arnaud Debussche, Da Prato, Giuseppe +1
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1412.7426

arxiv created 2014/12/23 · arxiv updated 2014/12/24

Abstract

We consider the Burgers equation on H=L²(0,1) perturbed by white noise and the corresponding transition semigroup P_t. We prove a new formula for P_tDφ (where φ:H→\R is bounded and Borel) which depends on φ but not on its derivative. Then we deduce some new consequences for the invariant measure ν of P_t as its Fomin differentiability and an integration by parts formula which generalises the classical one for gaussian measures.

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