The paper proves generalized integration by parts formulas for Bessel bridges with arbitrary boundary values and constructs a weak gradient dynamics for the two-dimensional Bessel bridge.
An It\^o type formula for the additive stochastic heat equation
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abstract
We use the theory of regularity structures to develop an It\^o 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 stochastic calculus.
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2019 1verdicts
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Bessel SPDEs with general Dirichlet boundary conditions
The paper proves generalized integration by parts formulas for Bessel bridges with arbitrary boundary values and constructs a weak gradient dynamics for the two-dimensional Bessel bridge.