Journal of Applied Mathematics and Stochastic Analysis
Volume 2007 (2007), Article ID 42640, 33 pages
On a Class of Forward-Backward Stochastic Differential Systems in Infinite Dimensions
Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milano 20133, Italy
Received 28 June 2006; Revised 27 February 2007; Accepted 14 April 2007
Copyright © 2007 Giuseppina Guatteri. 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 prove that a class of fully coupled forward-backward systems in infinite dimensions has a local unique solution. After studying the regularity property of the solution, we prove that for a peculiar class of systems arising in the theory of stochastic optimal control, the solution exists in arbitrary large time interval. Finally, we investigate the connection between the solution to the systems and a stochastic optimal control problem.