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arXiv · 1208.3709

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

N. V. Krylov
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Abstract

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.

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N. V. Krylov. 2012-08-18. A relatively short proof of It\^o's formula for SPDEs and its applications. https://arxiv.org/abs/1208.3709

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