An Itô type formula for the additive stochastic heat equation
Résumé
We use the recent theory of regularity structures to develop an It\^o formula for $u$, the stochastic heat equation with space-time white noise in one space dimension with periodic boundary conditions. In particular for any smooth enough function $\phi$ we can express the random distribution $(\partial_t-\partial_{xx})\phi(u)$ and the random field $\phi(u)$ in terms of the reconstruction of some modelled distributions. The law of the resulting objects is also identified with some classical constructions of stochastic calculus
Domaines
Probabilités [math.PR]Origine | Fichiers produits par l'(les) auteur(s) |
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