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January 2011 Feynman–Kac formula for heat equation driven by fractional white noise
Yaozhong Hu, David Nualart, Jian Song
Ann. Probab. 39(1): 291-326 (January 2011). DOI: 10.1214/10-AOP547


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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Yaozhong Hu. David Nualart. Jian Song. "Feynman–Kac formula for heat equation driven by fractional white noise." Ann. Probab. 39 (1) 291 - 326, January 2011.


Published: January 2011
First available in Project Euclid: 3 December 2010

zbMATH: 1210.60056
MathSciNet: MR2778803
Digital Object Identifier: 10.1214/10-AOP547

Primary: 35K20 , 35R60 , 60G17 , 60G22 , 60G30 , 60H07 , 60H15

Keywords: Absolute continuity , chaos expansion , exponential integrability , Feynman–Kac formula , Fractional noise , Hölder continuity , Stochastic heat equations

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.39 • No. 1 • January 2011
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