FEYNMAN-KAC FORMULA FOR HEAT EQUATION DRIVEN BY FRACTIONAL WHITE NOISE

• 成果类型: Article
• 署名作者: Hu, Yaozhong; Nualart, David; Song, Jian
• 署名单位: University of Kansas
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP547
• 发表日期: 2011
• 页码: 291-326
• 关键词: integration; calculus

摘要

We establish a version of the Feynman-Kac formula for the multidimensional stochastic heat equation with a multiplicative fractional Brownian sheet. We use the techniques of Malliavin calculus to prove that the process defined by the Feynman-Kac formula is a weak solution of the stochastic heat equation. From the Feynman-Kac formula, we establish the smoothness of the density of the solution and the Holder regularity in the space and time variables. We also derive a Feynman-Kac formula for the stochastic heat equation in the Skorokhod sense and we obtain the Wiener chaos expansion of the solution.