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Stochastic evolution equations with fractional Brownian motion
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  • Published: 04 July 2003

Stochastic evolution equations with fractional Brownian motion

  • S. Tindel1,
  • C.A. Tudor2 &
  • F. Viens3 

Probability Theory and Related Fields volume 127, pages 186–204 (2003)Cite this article

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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.

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Author information

Authors and Affiliations

  1. Département de Mathématiques, Institut Galilée, Université de Paris 13, Avenue J.-B. Clément, 93430, Villetaneuse, France

    S. Tindel

  2. Laboratoire de Probabilités, Université de Paris 6, 4, Place Jussieu, 75252, Paris Cedex 05, France

    C.A. Tudor

  3. Dept. Mathematics & Dept. Statistics, Purdue University, 1399 Math Sci Bldg, West Lafayette, IN, 47907, USA

    F. Viens

Authors
  1. S. Tindel
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  2. C.A. Tudor
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  3. F. Viens
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Corresponding author

Correspondence to F. Viens.

Additional information

Mathematics Subject Classification (2000): 60H15, 60G15

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Cite this article

Tindel, S., Tudor, C. & Viens, F. Stochastic evolution equations with fractional Brownian motion. Probab. Theory Relat. Fields 127, 186–204 (2003). https://doi.org/10.1007/s00440-003-0282-2

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  • Received: 08 October 2002

  • Revised: 25 April 2003

  • Published: 04 July 2003

  • Issue Date: October 2003

  • DOI: https://doi.org/10.1007/s00440-003-0282-2

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Key words or phrases:

  • Fractional Brownian motion
  • Stochastic partial differential equation
  • Hurst parameter
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