In this paper a new result on the existence and uniqueness of the adapted solution to a backward stochastic evolution equation in Hilbert spaces under non Lipschitz condition is established. The applicability of this result is then illustrated in a discussion of some concrete backward stochastic partial differential equation. Furthermore, stochastic maximum principle for optimal control problems of stochastic systems governed by backward stochastic evolution equations in Hilbert spaces is obtained.
Nonlinear Analysis Series A: Theory, Methods, and Applications
Mahmudov, N. I., & McKibben, M. A. (2007). On backward stochastic evolution equations in Hilbert space and optimal control. Nonlinear Analysis Series A: Theory, Methods, and Applications, 67(4), 1262-1274. Retrieved from https://digitalcommons.wcupa.edu/math_facpub/8