Bessel SPDEs and renormalised local times

• 成果类型: Article
• 署名作者: Altman, Henri Elad; Zambotti, Lorenzo
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-019-00926-0
• 发表日期: 2020
• 页码: 757-807
• 关键词: parts formulas; integration; equilibrium; equation

摘要

In this article, we prove integration by parts formulae (IbPFs) for the laws of Bessel bridges from 0 to 0 over the interval [0, 1] of dimension smaller than 3. As an application, we construct a weak version of a stochastic PDE having the law of a one-dimensional Bessel bridge (i.e. the law of a reflected Brownian bridge) as reversible measure, the dimension 1 being particularly relevant in view of applications to scaling limits of dynamical critical pinning models. We also exploit the IbPFs to conjecture the structure of the stochastic PDEs associated with Bessel bridges of all dimensions smaller than 3.