A Note on a Fenyman-Kac-Type Formula

Date
Authors
Balan, Raluca
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
In this article, we establish a probabilistic representation for the second-order moment of the solution of stochastic heat equation in $[0,1] \times \bR^d$, with multiplicative noise, which is fractional in time and colored in space. This representation is similar to the one given in Dalang, Mueller and Tribe (2008) in the case of an s.p.d.e. driven by a Gaussian noise, which is white in time. Unlike the formula of Dalang, Mueller and Tribe (2008), which is based on the usual Poisson process, our representation is based on the planar Poisson process, due to the fractional component of the noise.
Keywords
Mathematics - Probability, 60H15 (Primary), 60H05 (Secondary)
Citation
Collections