On a new version of the Ito's formula for the stochastic heat equation
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🧮 math.PR
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formulaequationheats-typestochasticderivedimensionaldiscuss
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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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