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Feynman-Kac formula for the heat equation driven by fractional white noise
Hu, Yaozhong Nualart, David Song, Jian
Hu, Yaozhong
Nualart, David
Song, Jian
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Abstract
We establish a version of the Feynman–Kac formula for the multidimensional stochastic heat equation with a multiplicative fractional Brownian sheet. We use the techniques of Malliavin calculus to prove that the process defined by the Feynman–Kac formula is a weak solution of the stochastic heat equation. From the Feynman–Kac formula, we establish the smoothness of the density of the solution and the Hölder regularity in the space and time variables. We also derive a Feynman–Kac formula for the stochastic heat equation in the Skorokhod sense and we obtain the Wiener chaos expansion of the solution.
Description
This is the published version, also available here: http://dx.doi.org/10.1214/10-AOP547.
Date
2011-02-01
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Institute of Mathematical Statistics
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Keywords
Fractional noise, stochastic heat equations, Feynman–Kac formula, exponential integrability, absolute continuity, Hölder continuity, chaos expansion
Citation
Hu, Yaozhong., Nualart, David., Song, Jian. "Feynman–Kac formula for heat equation driven by fractional white noise." Ann. Probab. Volume 39, Number 1 (2011), 291-326. http://dx.doi.org/10.1214/10-AOP547.