A nonlinear stochastic heat equation: Holder continuity and smoothness of the density of the solution

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Hu, Yaozhong¹  Nualart, David¹  Song, Jian² 

[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

[2] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA

关键词: Fractional noise;    Stochastic heat equations;    Feynman-Kac formula;    Exponential integrability;    Absolute continuity;    Holder continuity;    Chaos expansion;   

DOI  :  10.1016/j.spa.2012.11.004

来源: Elsevier

【 摘 要 】

In this paper, we establish a version of the Feynman-Kac formula for multidimensional stochastic heat equation driven by a general semimartingale. This Feynman-Kac formula is then applied to study some nonlinear stochastic heat equations driven by nonhomogeneous Gaussian noise: first, an explicit expression for the Malliavin derivatives of the solutions is obtained. Based on the representation we obtain the smooth property of the density of the law of the solution. On the other hand, we also obtain the Holder continuity of the solutions. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free