Journal of Applied Mathematics and Stochastic Analysis
Volume 2007 (2007), Article ID 69747, 26 pages
On a Class of Measure-Dependent Stochastic Evolution Equations Driven by fBm
1Departamento de Mathemática, I.C.M.C., Universidade de Sao Paulo, Caixa Postal 668, Sao Carlos 13560-970, SP, Brazil
2Department of Mathematics, Ohio University, Athens 45701, OH, USA
3Mathematics and Computer Science Department, Goucher College, Baltimore 21204, MD, USA
Received 2 January 2007; Revised 21 April 2007; Accepted 6 July 2007
Copyright © 2007 Eduardo Hernandez et al. 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.
We investigate a class of abstract stochastic evolution equations driven by a fractional Brownian motion (fBm) dependent upon a family of probability measures in a real separable Hilbert space. We establish the existence and uniqueness of a mild solution, a continuous dependence estimate, and various convergence and approximation results. Finally, the analysis of three examples is provided to illustrate the applicability of the general theory.