Open Access
2020 An Itô type formula for the additive stochastic heat equation
Carlo Bellingeri
Electron. J. Probab. 25: 1-52 (2020). DOI: 10.1214/19-EJP404


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.


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Carlo Bellingeri. "An Itô type formula for the additive stochastic heat equation." Electron. J. Probab. 25 1 - 52, 2020.


Received: 7 March 2018; Accepted: 15 December 2019; Published: 2020
First available in Project Euclid: 7 January 2020

zbMATH: 07149389
MathSciNet: MR4053902
Digital Object Identifier: 10.1214/19-EJP404

Primary: 60H15

Keywords: Itô formula , Malliavin calculus , Regularity structures , Stochastic partial differential equations

Vol.25 • 2020
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