A relatively short proof of itô’s formula for spdes and its applications

N. V. Krylov

doi:10.1007/s40072-013-0003-5

A relatively short proof of itô’s formula for spdes and its applications

N. V. Krylov

Mathematics

Research output: Contribution to journal › Article › peer-review

38 Scopus citations

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.

Original language	English (US)
Pages (from-to)	152-174
Number of pages	23
Journal	Stochastics and Partial Differential Equations: Analysis and Computations
Volume	1
Issue number	1
DOIs	https://doi.org/10.1007/s40072-013-0003-5
State	Published - Mar 2013

Bibliographical note

Funding Information:
The author is sincerely grateful to the referees for several comments which helped improve the presentation. The work was partially supported by NSF Grant DNS-1160569.

Publisher Copyright:
© Springer Science+Business Media New York 2013.

Keywords

Itô’s formula
Maximum principle
Stochastic partial differential equations

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A relatively short proof of itô’s formula for spdes and its applications

Abstract

Bibliographical note

Keywords

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