Mean-field backward stochastic evolution equations in Hilbert spaces and optimal control for BSPDEs
type: Item
instance of: scholarly article
title: Mean-field backward stochastic evolution equations in Hilbert spaces and optimal control for BSPDEs
zbMATH Open document ID: 1407.60090
DOI: 10.1155/2014/718948
author: Ruimin Xu
author: Tingting Wu
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: We obtain the existence and uniqueness result of the mild solutions to mean-field backward stochastic evolution equations (BSEEs) in Hilbert spaces under a weaker condition than the Lipschitz one. As an intermediate step, the existence and uniqueness result for the mild solutions of mean-field BSEEs under Lipschitz condition is also established. And then a maximum principle for optimal control problems governed by backward stochastic partial differential equations (BSPDEs) of mean-field type is presented. In this control system, the control domain need not to be convex and the coefficients, both in the state equation and in the cost functional, depend on the law of the BSPDE as well as the state and the control. Finally, a linear-quadratic optimal control problem is given to explain our theoretical results.
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 49K45
Mathematics Subject Classification ID: 93E20
zbMATH DE Number: 7017111
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/718948
OpenAlex ID: W1988991773
Wikidata QID: Q59071623
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description: scientific article; zbMATH DE number 7017111