KOLMOGOROV EQUATION ASSOCIATED TO THE STOCHASTIC REFLECTION PROBLEM ON A SMOOTH CONVEX SET OF A HILBERT SPACE

• 成果类型: Article
• 署名作者: Barbu, Viorel; Da Prat, Giuseppe; Tubaro, Luciano
• 署名单位: Alexandru Ioan Cuza University; Scuola Normale Superiore di Pisa; University of Trento
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/08-AOP438
• 发表日期: 2009
• 页码: 1427-1458
• 关键词: variational-inequalities; spdes

摘要

We consider the stochastic reflection problem associated with a self-adjoint operator A and a cylindrical Wiener process on a convex set K with nonempty interior and regular boundary Sigma in a Hilbert space H. We prove the existence and uniqueness of a smooth solution for the corresponding elliptic infinite-dimensional Kolmogorov equation with Neumann boundary condition on Sigma.