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

N. V. Krylov

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

Probability 2012-08-21 v1

Authors: N. V. Krylov

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.

Keywords

Itô's formula stochastic partial differential equations Hilbert-space valued processes Gelfand triple maximum principle stochastic differentials

Cite

@article{arxiv.1208.3709,
  title  = {A relatively short proof of It\^o's formula for SPDEs and its applications},
  author = {N. V. Krylov},
  journal= {arXiv preprint arXiv:1208.3709},
  year   = {2012}
}

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20 pages

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