Two-point Correlation Function and Feynman-Kac Formula for the Stochastic Heat Equation

作     者：Chen, Le Hu, Yaozhong Nualart, David 

作者机构：Univ Kansas Dept Math Lawrence KS 66045 USA 

出 版 物：《POTENTIAL ANALYSIS》 (位势分析)

年 卷 期：2017年第46卷第4期

页      面：779-797页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Swiss National Science Foundation [P2ELP2_151796] Simons Foundation NSF [DMS1512891] ARO [FED0070445] Direct For Mathematical & Physical Scien Division Of Mathematical Sciences Funding Source: National Science Foundation Swiss National Science Foundation (SNF) [P2ELP2_151796] Funding Source: Swiss National Science Foundation (SNF) 

主　　题：Stochastic heat equation Two-point correlation function Feynman-Kac formula Brownian local time Malliavin calculus 

摘      要：In this paper, we obtain an explicit formula for the two-point correlation function for the solutions to the stochastic heat equation on . The bounds for p-th moments proved in Chen and Dalang (Ann. Probab. 2015) are simplified. We validate the Feynman-Kac formula for the p-point correlation function of the solutions to this equation with measure-valued initial data.