Abstract
We use the theory of regularity structures to develop an Itô formula for $u$, the solution of the one-dimensional stochastic heat equation driven by space-time white noise with periodic boundary conditions. In particular, for any smooth enough function $\varphi $ we can express the random distribution $(\partial _{t}-\partial _{xx})\varphi (u)$ and the random field $\varphi (u)$ in terms of the reconstruction of some modelled distributions. The resulting objects are then identified with some classical constructions of Malliavin calculus.
Citation
Carlo Bellingeri. "An Itô type formula for the additive stochastic heat equation." Electron. J. Probab. 25 1 - 52, 2020. https://doi.org/10.1214/19-EJP404
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