An Itô type formula for the additive stochastic heat equation
Résumé
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 φ we can express the random distribution (∂t−∂xx)φ(u) and the random field φ(u) in terms of the reconstruction of some modelled distributions. The resulting objects are then identified with some classical constructions of Malliavin calculus.
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