Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1155704 | Stochastic Processes and their Applications | 2013 | 21 Pages |
Abstract
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 Hölder continuity of the solutions.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Yaozhong Hu, David Nualart, Jian Song,