Stochastic Maximum Principle for Optimal Control ofPartial Differential Equations Driven by White Noise

Marco Fuhrman (1) , Ying Hu (2) , Gianmario Tessitore (3)

1 Dipartimento di Matematica "F. Brioschi"
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 Dipartimento di Matematica e Applicazioni [Milano]

We prove a stochastic maximum principle ofPontryagin's type for the optimal control of a stochastic partial differential equationdriven by white noise in the case when the set of control actions is convex. Particular attention is paid to well-posedness of the adjoint backward stochastic differential equation and the regularity properties of its solution with values in infinite-dimensional spaces.

Mots clés: Stochastic partial differential equations; backward stochastic partial differential equations; Stochastic optimal control; White noise; Stochastic maximum principle

Domaines: Probabilités [math.PR]; Optimisation et contrôle [math.OC]

Marco Fuhrman, Ying Hu, Gianmario Tessitore. Stochastic Maximum Principle for Optimal Control ofPartial Differential Equations Driven by White Noise. Stochastics and Partial Differential Equations: Analysis and Computations, 2018, 6 (2), pp.255-285. ⟨10.1007/s40072-017-0108-3⟩. ⟨hal-01064475v2⟩