Journal of Applied Mathematics and Stochastic Analysis 
Volume 2007 (2007), Article ID 69747, 26 pages
doi:10.1155/2007/69747
Research Article

On a Class of Measure-Dependent Stochastic Evolution Equations Driven by fBm

Eduardo Hernandez,1 David N. Keck,2 and Mark A. McKibben3

 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

Abstract

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.