Journal of Applied Mathematics and Stochastic Analysis
Volume 16 (2003), Issue 2, Pages 141-161
Functional integro-differential stochastic evolution equations in
1Ohio University, Department of Mathematics, 321 Morton Hall, Athens 45701, OH, USA
2Goucher College, Department of Mathematics and Computer Science, 1021 Dulaney Valley Road, Baltimore 21204, MD, USA
Received 1 September 2002; Revised 1 February 2003
Copyright © 2003 David N. Keck and Mark A. McKibben. 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 functional integro-differential stochastic evolution equations in a real separable Hilbert space. Global existence results concerning mild and periodic solutions are formulated under various growth and compactness conditions. Also, related convergence results are established and an example arising in the mathematical modeling of heat conduction is discussed to illustrate the abstract theory.