A version of Hörmander's theorem in 2-smooth Banach spaces

Abstract

We consider a stochastic evolution equation in a 2-smooth Banach space with a densely and continuously embedded Hilbert subspace. We prove that under Hörmander's bracket condition, the image measure of the solution law under any finite-rank bounded linear operator is absolutely continuous with respect to the Lebesgue measure. To obtain this result, we apply methods of the Malliavin calculus.

References in corpus (2)

• $\gamma$-Radonifying operators -- a survey
• Tools for Malliavin calculus in UMD Banach spaces