Yaozhong Hu, David Nualart, Jian Song
Published 2009-06-17, updated 2010-12-09Version 2
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 H\"{o}lder 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.
Comments: Published in at http://dx.doi.org/10.1214/10-AOP547 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Journal: Annals of Probability 2011, Vol. 39, No. 1, 291-326
Feynman--Kac formula for the heat equation driven by fractional noise with Hurst parameter $H<1/2$
Simulating diffusion bridges using the Wiener chaos expansion
On the Wiener Chaos Expansion of the Signature of a Gaussian Process
![QR code for arXiv:0906.3076 [math.PR]](http://oss.arxitics.com/images/favicon.svg)