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

N. V. Krylov

Published 2012-08-18Version 1

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