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General necessary conditions for partially observed optimal stochastic controls

Part of: Stochastic systems and control Stochastic processes Stochastic analysis

Published online by Cambridge University Press:  14 July 2016

Xunjing Li  and
Shanjian Tang
Xunjing Li*
Affiliation:
Fudan University
Shanjian Tang*
Affiliation:
Fudan University
*
∗Postal address: Department of Mathematics, Fudan University, Shanghai 200433, People's Republic of China.
∗Postal address: Department of Mathematics, Fudan University, Shanghai 200433, People's Republic of China.
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Abstract

The partially observed control problem is considered for stochastic processes with control entering into the diffusion and the observation. The maximum principle is proved for the partially observable optimal control. A pure probabilistic approach is used, and the adjoint processes are characterized as solutions of related backward stochastic differential equations in finite-dimensional spaces. Most of the derivation is identified with that of the completely observable case.

Keywords

MAXIMUM PRINCIPLEPARTIAL OBSERVATIONFIRST AND SECOND ADJOINT PROCESSES

MSC classification

Primary: 93E20: Optimal stochastic control
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.) 60G35: Signal detection and filtering
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 4 , December 1995 , pp. 1118 - 1137
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Research partially supported by the NSF of China and the Chinese State Education Commission Science Foundation.

References

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