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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


SCImago Journal Rank (SJR) 2015: 0.398
Source Normalized Impact per Paper (SNIP) 2015: 0.949
Impact per Publication (IPP) 2015: 0.408

Mathematical Citation Quotient (MCQ) 2015: 0.22

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1569-397X
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On the law of the solution to a stochastic heat equation with fractional noise in time

1Carnegie Mellon University, Department of Mathematical Sciences, Pittsburgh, PA 15213, USA

2Laboratoire Paul Painlevé, Université de Lille 1, F-59655 Villeneuve d'Ascq, France

Funding Source: ANR

Award identifier / Grant number: “Masterie” BLAN 012103

Citation Information: Random Operators and Stochastic Equations. Volume 23, Issue 3, Pages 179–186, ISSN (Online) 1569-397X, ISSN (Print) 0926-6364, DOI: https://doi.org/10.1515/rose-2014-0038, August 2015

Publication History

Received:
2014-03-31
Accepted:
2015-04-22
Published Online:
2015-08-13

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

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