Feynman-Kac formula for the heat equation driven by fractional white noise

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Issue Date
2011-02-01Author
Hu, Yaozhong
Nualart, David
Song, Jian
Publisher
Institute of Mathematical Statistics
Type
Article
Article Version
Scholarly/refereed, publisher version
Metadata
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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.
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This is the published version, also available here: http://dx.doi.org/10.1214/10-AOP547.
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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.
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