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Probability Theory and Related Fields

, Volume 127, Issue 2, pp 186–204 | Cite as

Stochastic evolution equations with fractional Brownian motion

Article

Abstract.

In this paper linear stochastic evolution equations driven by infinite-dimensional fractional Brownian motion are studied. A necessary and sufficient condition for the existence and uniqueness of the solution is established and the spatial regularity of the solution is analyzed; separate proofs are required for the cases of Hurst parameter above and below 1/2. The particular case of the Laplacian on the circle is discussed in detail.

Key words or phrases:

Fractional Brownian motion Stochastic partial differential equation Hurst parameter 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Département de Mathématiques, Institut GaliléeUniversité de Paris 13VilletaneuseFrance
  2. 2.Laboratoire de ProbabilitésUniversité de Paris 6Paris Cedex 05France
  3. 3.Dept. Mathematics & Dept. StatisticsPurdue UniversityWest LafayetteUSA

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