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2009 A Note on a Feynman-Kac-Type Formula
Raluca Balan
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Electron. Commun. Probab. 14: 252-260 (2009). DOI: 10.1214/ECP.v14-1468


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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Raluca Balan. "A Note on a Feynman-Kac-Type Formula." Electron. Commun. Probab. 14 252 - 260, 2009.


Accepted: 25 June 2009; Published: 2009
First available in Project Euclid: 6 June 2016

zbMATH: 1190.60049
MathSciNet: MR2516260
Digital Object Identifier: 10.1214/ECP.v14-1468

Primary: 60H15
Secondary: 60H05

Keywords: Feynman-Kac formula , fractional Brownian motion , planar Poisson process , Stochastic heat equation

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