On the law of the solution to a stochastic heat equation with fractional noise in time:

Solesne Bourguin; Ciprian A. Tudor

doi:10.1515/rose-2014-0038

Published by De Gruyter August 13, 2015

On the law of the solution to a stochastic heat equation with fractional noise in time

Solesne Bourguin and Ciprian A. Tudor

From the journal Random Operators and Stochastic Equations

https://doi.org/10.1515/rose-2014-0038

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Abstract

We study the law of the solution to the stochastic heat equation with additive Gaussian noise which behaves as the fractional Brownian motion in time and is white in space. We prove a decomposition of the solution in terms of the bifractional Brownian motion. Our result is an extension of a result by Swanson.

Keywords: Stochastic heat equation; Gaussian noise; bifractional Brownian motion

MSC: 60H15; 60H05

Funding source: ANR

Award Identifier / Grant number: “Masterie” BLAN 012103

Received: 2014-3-31

Accepted: 2015-4-22

Published Online: 2015-8-13

Published in Print: 2015-9-1

On the law of the solution to a stochastic heat equation with fractional noise in time

Abstract

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