Mean-Field Backward Stochastic Evolution Equations in Hilbert Spaces and Optimal Control for BSPDEs
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-07-13
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Xu, Ruimin& Wu, Tingting. 2014. Mean-Field Backward Stochastic Evolution Equations in Hilbert Spaces and Optimal Control for BSPDEs. Mathematical Problems in Engineering،Vol. 2014, no. 2014, pp.1-18.
https://search.emarefa.net/detail/BIM-493122
Modern Language Association (MLA)
Xu, Ruimin& Wu, Tingting. Mean-Field Backward Stochastic Evolution Equations in Hilbert Spaces and Optimal Control for BSPDEs. Mathematical Problems in Engineering No. 2014 (2014), pp.1-18.
https://search.emarefa.net/detail/BIM-493122
American Medical Association (AMA)
Xu, Ruimin& Wu, Tingting. Mean-Field Backward Stochastic Evolution Equations in Hilbert Spaces and Optimal Control for BSPDEs. Mathematical Problems in Engineering. 2014. Vol. 2014, no. 2014, pp.1-18.
https://search.emarefa.net/detail/BIM-493122
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-493122