Journal of Applied Mathematics and Stochastic Analysis
Volume 2007 (2007), Article ID 42640, 33 pages
doi:10.1155/2007/42640
Abstract
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.