Optimal Control with State Constraints for Stochastic Evolution Equation with Jumps in Hilbert Space

This paper studies a stochastic optimal control problem with state constraint, where the state equation is described by a controlled stochastic evolution equation with jumps in Hilbert Space and the control domain is assumed to be convex. By means of Ekland variational principle, combining the convex variation method and the duality technique, necessary conditions for optimality are derived in the form of stochastic maximum principles.