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Abstract and Applied Analysis
Volume 2014, Article ID 516853, 14 pages
http://dx.doi.org/10.1155/2014/516853
Research Article

Abstract Functional Stochastic Evolution Equations Driven by Fractional Brownian Motion

1Department of Mathematics, West Chester University of Pennsylvania, 25 University Avenue, West Chester, PA 19383, USA
2Department of Mathematics and Computer Science, Goucher College, 1021 Dulaney Valley Road, Baltimore, MD 21204, USA

Received 21 October 2013; Revised 15 December 2013; Accepted 20 December 2013; Published 25 February 2014

Academic Editor: T. Diagana

Copyright © 2014 Mark A. McKibben and Micah Webster. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate a class of abstract functional stochastic evolution equations driven by a fractional Brownian motion in a real separable Hilbert space. Global existence results concerning mild solutions are formulated under various growth and compactness conditions. Continuous dependence estimates and convergence results are also established. Analysis of three stochastic partial differential equations, including a second-order stochastic evolution equation arising in the modeling of wave phenomena and a nonlinear diffusion equation, is provided to illustrate the applicability of the general theory.