A Note on a Feynman-Kac-Type Formula
Raluca M Balan, University of Ottawa
Abstract
In this article, we establish a probabilistic representation for the second-order moment of the solution of stochastic heat equation, 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.
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