A Note on a Fenyman-Kac-Type Formula

2009/05/16 by Raluca M. Balan, Raluca Balan, Balan, Raluca
Mathematics · #Advanced Algebra and Geometry #Random Matrices and Applications #advanced mathematical theories #math.PR #msc:60H05 #msc:60H15

paper · pdf · doi:10.48550/arxiv.0905.2698

arxiv created 2009/05/16 · arxiv updated 2009/12/01

Abstract

In this article, we establish a probabilistic representation for the second-order moment of the solution of stochastic heat equation in [0,1] × \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.

Citations

• Stochastic Heat Equation with Multiplicative Fractional-Colored Noise

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