Estimate for P t D for the stochastic Burgers equation

Giuseppe da Prato (1) , Arnaud Debussche (2)

1 SNS - Scuola Normale Superiore di Pisa
2 MINGUS - Multi-scale numerical geometric schemes

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 t Dϕ (where ϕ : H → R is bounded and Borel) which depends on ϕ but not on its derivative. Then we deduce some 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.

Domaines: Probabilités [math.PR]

Giuseppe da Prato, Arnaud Debussche. Estimate for P t D for the stochastic Burgers equation. 2019. ⟨hal-02347398⟩