A relatively short proof of Itô's formula for SPDEs and its applications

Abstract

We give a short proof of Itô's formula for stochastic Hilbert-space valued processes in the setting $V\subset H\subset V^{\ast }$ based on the possibility to lift the stochastic differentials, which are originally in $V^{\ast }$, into $H$. Using this result we also prove the maximum principle for second-order SPDEs in arbitrary domains.

20 pages