Feynman-Kac formula for heat equation driven by fractional white noise
pith:44K5RSZD Add to your LaTeX paper
What is a Pith Number?\usepackage{pith}
\pithnumber{44K5RSZD}
Prints a linked pith:44K5RSZD badge after your title and writes the identifier into PDF metadata. Compiles on arXiv with no extra files. Learn more
read the original 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 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.
This paper has not been read by Pith yet.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.