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

2012/08/18 by Krylov, N. V. · 1 citation
#35R60 #60H15 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1208.3709

Abstract

We give a short proof of Itô's formula for stochastic Hilbert-space valued processes in the setting V⊂ H⊂ 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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