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

Yaozhong Hu, David Nualart and Jian Song

Stochastic Processes and their Applications, 2013, vol. 123, issue 3, 1083-1103

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.

Keywords: Fractional noise; Stochastic heat equations; Feynman–Kac formula; Exponential integrability; Absolute continuity; Hölder continuity; Chaos expansion (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2012.11.004

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