Evolution equations driven by a fractional Brownian motion |
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Authors: | Bohdan Maslowski David Nualart |
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Institution: | a Institute of Mathematics, Academy of Sciences of Czech Republic, Prague, Czech Republic b Universitat de Barcelona, Facultat de Matemàtiques, Gran Via, 585, 08007 Barcelona, Spain |
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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 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 . The proofs of our results combine techniques of fractional calculus with semigroup estimates. |
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