Estimate for PₜD for the stochastic Burgers equation

الأصل · EN

We consider the Burgers equation on H=L²(0,1) perturbed by white noise and the corresponding transition semigroup Pₜ. We prove a new formula for PₜDφ (where φ:H→ 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 Pₜ as its Fomin differentiability and an integration by parts formula which generalises the classical one for gaussian measures.