Feynman-Kac formula for the heat equation driven by fractional noise with Hurst parameter H < 1/2

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Issue Date
2012-09-01Author
Hu, Yaozhong
Lu, Fei
Nulart, David
Publisher
Institute of Mathematical Statistics
Type
Article
Article Version
Scholarly/refereed, publisher version
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In this paper, a Feynman–Kac formula is established for stochastic partial differential equation driven by Gaussian noise which is, with respect to time, a fractional Brownian motion with Hurst parameter H < 1/2. To establish such a formula, we introduce and study a nonlinear stochastic integral from the given Gaussian noise. To show the Feynman–Kac integral exists, one still needs to show the exponential integrability of nonlinear stochastic integral. Then, the approach of approximation with techniques from Malliavin calculus is used to show that the Feynman–Kac integral is the weak solution to the stochastic partial differential equation.
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This is the published version, also available here: http://dx.doi.org/10.1214/11-AOP649.
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Citation
Hu, Yaozhong., Lu, Fei., Nualart, David. "Feynman-Kac formula for the heat equation driven by fractional noise with Hurst parameter H < 1/2." Ann. Probab. Volume 40, Number 3 (2012), 1041-1068. http://dx.doi.org/10.1214/11-AOP649.
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