A version of H\"ormander's theorem in 2-smooth Banach spaces
Probability
2013-04-17 v2
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 H\"ormander'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.
Cite
@article{arxiv.1304.3688,
title = {A version of H\"ormander's theorem in 2-smooth Banach spaces},
author = {Evelina Shamarova},
journal= {arXiv preprint arXiv:1304.3688},
year = {2013}
}