Stochastic maximum principle for optimal control of partial differential equations driven by white noise

被引：9

作者：

Fuhrman, Marco ^{[1
]}

Hu, Ying ^{[2
]}

Tessitore, Gianmario ^{[3
]}

机构：

[1] Univ Milan, Dipartimento Matemat, Via Saldini 50, I-20133 Milan, Italy

[2] Univ Rennes 1, IRMAR, Campus Beaulieu, F-35042 Rennes, France

[3] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, Via Cozzi 53, I-20125 Milan, Italy

来源：

STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS | 2018年 / 6卷 / 02期

关键词：

Stochastic maximum principle; Stochastic partial differential equations; Backward stochastic partial differential equations; Stochastic optimal control; White noise; INFINITE-DIMENSIONAL SPACES; SYSTEMS; SPDES;

D O I：

10.1007/s40072-017-0108-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a stochastic maximum principle of Pontryagin's type for the optimal control of a stochastic partial differential equation driven 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.

引用

页码：255 / 285

页数：31

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