A relatively short proof of It\^o's formula for SPDEs and its applications

摘要

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