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)|
|Number of pages||23|
|Journal||Stochastics and Partial Differential Equations: Analysis and Computations|
|State||Published - Mar 2013|
Bibliographical noteFunding 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.
© Springer Science+Business Media New York 2013.
- Itô’s formula
- Maximum principle
- Stochastic partial differential equations