We derive an It^o's-type formula for the one dimensional stochastic heat equation driven by a space-time white noise. The proof is based on elementary properties of the S-transform and on the explicit representation of the solution process. We also discuss the relationship with other versions of this It^o formula existing in literature.

White noise approach to the Itˆo formula for the stochastic heat equation

LANCONELLI, ALBERTO
2007

Abstract

We derive an It^o's-type formula for the one dimensional stochastic heat equation driven by a space-time white noise. The proof is based on elementary properties of the S-transform and on the explicit representation of the solution process. We also discuss the relationship with other versions of this It^o formula existing in literature.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11586/20282
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