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

作者：Hu Yaozhong; Nualart David; Song Jian^*

来源：Stochastic Processes and Their Applications, 2013, 123(3): 1083-1103.

DOI：10.1016/j.spa.2012.11.004

• Fractional noise
• Stochastic heat equations
• Feynman-Kac formula
• Exponential integrability
• Absolute continuity
• Holder continuity
• Chaos expansion

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.

• 出版日期2013-3
• 单位rutgers