On a new version of the Ito's formula for the stochastic heat equation

Mathematics – Probability

Scientific paper

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10 pages

Scientific paper

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 $\mathcal{S}$-transform and on the explicit representation of
the solution process. We also discuss the relationship with other versions of
this It\^o's-type formula existing in literature.

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