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Random Operators and Stochastic Equations

Editor-in-Chief: Girko, Vyacheslav

Managing Editor: Molchanov, S.

Editorial Board Member: Accardi, L. / Albeverio, Sergio / Carmona, R. / Casati, G. / Christopeit, N. / Domanski, C. / Drygas, Hilmar / Gupta, A.K. / Ibragimov, I. / Kirsch, Werner / Klein, A. / Kondratyev, Yuri / Kurotschka, V. / Leonenko, N. / Loubaton, Philippe / Orsingher, E. / Pastur, L. / Rodrigues, Waldyr A. / Shiryaev, Albert / Turbin, A.F. / Veretennikov, Alexandre

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Volume 23, Issue 3 (Sep 2015)


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

Solesne Bourguin
  • Corresponding author
  • Carnegie Mellon University, Department of Mathematical Sciences, Pittsburgh, PA 15213, USA
  • Email:
/ Ciprian A. Tudor
  • Laboratoire Paul Painlevé, Université de Lille 1, F-59655 Villeneuve d'Ascq, France
  • Email:
Published Online: 2015-08-13 | DOI: https://doi.org/10.1515/rose-2014-0038


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

About the article

Received: 2014-03-31

Accepted: 2015-04-22

Published Online: 2015-08-13

Published in Print: 2015-09-01

Funding Source: ANR

Award identifier / Grant number: “Masterie” BLAN 012103

Citation Information: Random Operators and Stochastic Equations, ISSN (Online) 1569-397X, ISSN (Print) 0926-6364, DOI: https://doi.org/10.1515/rose-2014-0038. Export Citation

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