Integration by parts formulae on convex sets of paths and applications to SPDEs with reflection
type: Item
instance of: scholarly article
title: Integration by parts formulae on convex sets of paths and applications to SPDEs with reflection
zbMATH Open document ID: 1009.60047
author: L. Zambotti
publication date: 2002-12-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 31C25
zbMATH DE Number: 1837001
zbMATH Keywords: integration by parts
zbMATH Keywords: stochastic partial differential equations with reflection
zbMATH Keywords: additive functionals
zbMATH Keywords: Dirichlet processes
reviewed by: Jean Picard
MaRDI profile type: Publication
full work available at URL: s004400200203
OpenAlex ID: W2046674598
DOI: 10.1007/S004400200203
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 1837001