An Itô type formula for the additive stochastic heat equation

Carlo Bellingeri (1)

1 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

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]

Carlo Bellingeri. An Itô type formula for the additive stochastic heat equation. 2018. ⟨hal-01725871v1⟩