Necessary conditions for optimality for stochastic evolution equations

2012/10/24 by AbdulRahman Al-Hussein, Al-Hussein, AbdulRahman
Computer Science · Economics, Econometrics and Finance · Engineering · #60H10 #60H15 #93E20 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1210.6523

openalex publication_date 2012/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with providing the maximum principle for a control problem governed by a stochastic evolution system on a separable Hilbert space. In particular, necessary conditions for optimality for this stochastic optimal control problem are derived by using the adjoint backward stochastic evolution equation. Moreover, all coefficients appearing in this system are allowed to depend on the control variable. We achieve our results through the semigroup approach.

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