Integration by parts formulae on convex sets of paths and applications to SPDEs with reflection
Let \(K_\alpha\), \(\alpha\geq 0\), be the set of paths from \([0,1]\) into \([-\alpha,\infty)\). Integration by parts formulae are proved for the integration on \(K_0\) with respect to the Bessel bridge of dimension 3, and for the integration on \(K_\alpha\) with respect to the Brownian bridge. These formulae involve boundary terms with boundary measures \(\sigma_0\) and \(\sigma_\alpha\) which are explicited. They can be applied to the study of a family (indexed by \(\alpha\)) of stochastic partial differential equations (SPDE) with reflection which was introduced by Nualart and Pardoux. For instance, the solution of the SPDE can be viewed as the diffusion associated to a symmetric Dirichlet form on \(K_\alpha\); the reflection term of the SPDE and the boundary measure \(\sigma_\alpha\) can also be related.
stochastic partial differential equations with reflection
scientific article; zbMATH DE number 1837001