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Stochastic evolution equations driven by Liouville fractional Brownian motion |
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| Authors: | Zdzis?aw Brze?niak Jan van Neerven Donna Salopek |
| Affiliation: | 1. Department of Mathematics, University of York, York, YO10 5DD, UK 2. Delft Institute of Applied Mathematics, Delft University of Technology, P.O. Box 5031, 2600 GA, Delft, The Netherlands 3. School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia |
| Abstract: | Let H be a Hilbert space and E a Banach space. We set up a theory of stochastic integration of ℒ(H,E)-valued functions with respect to H-cylindrical Liouville fractional Brownian motion with arbitrary Hurst parameter 0 < β < 1. For 0 < β < ? we show that a function Φ: (0, T) → ℒ(H,E) is stochastically integrable with respect to an H-cylindrical Liouville fractional Brownian motion if and only if it is stochastically integrable with respect to an H-cylindrical fractional Brownian motion. |
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