Evolution equations driven by a fractional Brownian motion

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Abstract

In this paper we study nonlinear stochastic evolution equations in a Hilbert space driven by a cylindrical fractional Brownian motion with Hurst parameter H > 1/2 and nuclear covariance operator. We establish the existence and uniqueness of a mild solution under some regularity and boundedness conditions on the coefficients and for some values of the parameter H. This result is applied to stochastic parabolic equation perturbed by a fractional white noise. In this case, if the coefficients are Lipschitz continuous and bounded the existence and uniqueness of a solution holds if H > d/4. The proofs of our results combine techniques of fractional calculus with semigroup estimates. © 2002 Elsevier Inc. All rights reserved.

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Maslowski, B., & Nualart, D. (2003). Evolution equations driven by a fractional Brownian motion. Journal of Functional Analysis, 202(1), 277–305. https://doi.org/10.1016/S0022-1236(02)00065-4

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