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

TL;DR

This paper develops stochastic maximum principles for optimal control problems with state constraints involving stochastic evolution equations with jumps in Hilbert spaces, using variational and duality methods.

Contribution

It introduces necessary optimality conditions for control problems with jumps in infinite-dimensional spaces, extending existing theories with new variational techniques.

Findings

Derived stochastic maximum principles for jump-diffusion evolution equations

Established necessary conditions for optimal control with state constraints

Extended control theory to infinite-dimensional Hilbert space settings

Abstract

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.