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18 (1) (2005), 109–120. [20] B. Mandelbrot and J. , 10 (1968), 422–437. [21] D. Matignon and G. Montseny, editors. Syst`emes Diff´ erentiels Fractionnaires, volume 5 of ESAIM Proceedings, Paris, 1998. Soci´et´e de Math´ematiques Appliqu´ees et Industrielles. [22] I. Norros, E. Valkeila, and J. Virtamo, An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions, Bernoulli, 5 (4) (1999), 571–587. [23] V. S. Taqqu, Integration questions related to fractional Brownian motion, Probab.

Villani, Topics in Mass Transportation, Graduate studies in Mathematics, AMS, 2003. fr Progress in Probability, Vol. 59, 23–36 c 2007 Birkh¨ auser Verlag Basel/Switzerland Stationary Solutions for the 2D Stochastic Dissipative Euler Equation Hakima Bessaih Abstract. A 2-dimensional dissipative Euler equation, subject to a random perturbation is considered. Using compactness arguments, existence of martingale stationary solutions are proved. Mathematics Subject Classification (2000). Primary 60H15; Secondary 60G10.

1 which concernes with the estimate of the L2 -norm of the stochastic convolution process; several applications are given in Section 3 where, in particular, we shall consider the following classes of kernels. 2. 1. The kernel K(t, s) is of fractional integration type: K(t, s) = gϑ (t − s) for some ϑ > 12 ; this case naturally arises in evolution equations of fractional order in time, compare for instance [5]; the main advantage of working with this kernel is the simplicity in the computations; however, this filter does not preserve the stationary increment property of the input and it changes the self-similarity index.

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