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

N. V. Krylov

Research output: Contribution to journalArticlepeer-review

20 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 languageEnglish (US)
Pages (from-to)152-174
Number of pages23
JournalStochastics and Partial Differential Equations: Analysis and Computations
Volume1
Issue number1
DOIs
StatePublished - 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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