Necessary conditions for stochastic optimal control problems in infinite dimensions

• Published in: Stochastic processes and their applications Vol. 130; no. 7; pp. 4081 - 4103
• Main Authors: Frankowska, Hélène, Zhang, Xu
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2020; Elsevier
• Subjects: Adjoint equation; First and second order necessary optimality conditions; Mathematics; Maximum principle; Optimization and Control; Probability; Stochastic optimal control; Transposition solution; Variational equation; 93E20; Adjoint equation; 49J53; First and second order necessary optimality conditions; Variational equation; Stochastic optimal control; Maximum principle; 60H15; Transposition solution

The purpose of this paper is to establish the first and second order necessary conditions for stochastic optimal controls in infinite dimensions. The control system is governed by a stochastic evolution equation, in which both drift and diffusion terms may contain the control variable and the set of...