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Forward and Backward Mean-Field Stochastic Partial Differential Equation and Optimal Control |
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Citation: |
Maoning TANG,Qingxin MENG,Meijiao WANG.Forward and Backward Mean-Field Stochastic Partial Differential Equation and Optimal Control[J].Chinese Annals of Mathematics B,2019,40(4):515~540 |
Page view: 1207
Net amount: 1544 |
Authors: |
Maoning TANG; Qingxin MENG;Meijiao WANG |
Foundation: |
This work was supported by the National Natural Science
Foundation of China (Nos.11871121, 11471079, 11301177) and the
Natural Science Foundation of Zhejiang Province for Distinguished
Young Scholar (No.LR15A010001). |
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Abstract: |
This paper is mainly concerned with the solutions to both forward
and backward mean-field stochastic partial differential equation and
the corresponding optimal control problem for mean-field stochastic
partial differential equation. The authors first prove the
continuous dependence theorems of forward and backward mean-field
stochastic partial differential equations and show the existence
and uniqueness of solutions to them. Then they establish necessary
and sufficient optimality conditions of the control problem in the
form of Pontryagin's maximum principles. To illustrate the
theoretical results, the authors apply stochastic maximum principles
to study the infinite-dimensional linear-quadratic control problem
of mean-field type. Further, an application to a Cauchy problem for
a controlled stochastic linear PDE of mean-field type is studied. |
Keywords: |
Mean-field, Stochastic partial differential equation, Backwardstochastic partial differential equation, Optimal control, Maximumprinciple, Adjoint equation |
Classification: |
60H15, 35R60, 93E20 |
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