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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Mathematics Subject Classification (2000): 60H15, 60G15
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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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DOI: https://doi.org/10.1007/s00440-003-0282-2