Cauchy-Dirichlet problems for a class of hypoelliptic equation in $\R^d$: q new probabilistic representation formula for the gradient of the solutions

Giuseppe Da Prato; Luciano Tubaro

paper

Cauchy-Dirichlet problems for a class of hypoelliptic equation in $R^{d}$ : q new probabilistic representation formula for the gradient of the solutions

arXiv:2107.02502

Abstract

We prove the existence and a new representation formula for the gradient of the semigroup associated to an Ornstein-Uhlenbeck in a bounded convex domain in d dimensions.

23 pages

Cauchy-Dirichlet problems for a class of hypoelliptic equation in Rd: q new probabilistic representation formula for the gradient of the solutions

Abstract

Cauchy-Dirichlet problems for a class of hypoelliptic equation in $R^{d}$ : q new probabilistic representation formula for the gradient of the solutions