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) |
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Pages (from-to) | 152-174 |
Number of pages | 23 |
Journal | Stochastics and Partial Differential Equations: Analysis and Computations |
Volume | 1 |
Issue number | 1 |
DOIs | |
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