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Stochastic evolution equations with fractional Brownian motion
Authors:S?Tindel  CA?Tudor  Email author" target="_blank">F?ViensEmail author
Institution:(1) Département de Mathématiques, Institut Galilée, Université de Paris 13, Avenue J.-B. Clément, 93430 Villetaneuse, France;(2) Laboratoire de Probabilités, Université de Paris 6, 4, Place Jussieu, 75252 Paris Cedex 05, France;(3) Dept. Mathematics & Dept. Statistics, Purdue University, 1399 Math Sci Bldg, West Lafayette, IN 47907, USA
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. Mathematics Subject Classification (2000): 60H15, 60G15
Keywords:Fractional Brownian motion  Stochastic partial differential equation  Hurst parameter
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