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
2007-01-01
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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
