Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/19347
Title: Optimal control of point processes with noisy observations : the maximum principle
Authors: Tang, S
Hou, SH
Keywords: Adjoint vector fields
Backward stochastic integral-partial differential equations
Maximum principle
Partially observed optimal control
Point processes
Issue Date: 2002
Publisher: Springer
Source: Applied mathematics and optimization, 2002, v. 45, no. 2, p. 185-212 How to cite?
Journal: Applied Mathematics and Optimization 
Abstract: This paper studies the optimal control problem for point processes with Gaussian white-noised observations. A general maximum principle is proved for the partially observed optimal control of point processes, without using the associated filtering equation. Adjoint flow - the adjoint processes of the stochastic flows of the optimal system - are introduced, and their relations are established. Adjoint vector fields, which are observation-predictable, are introduced as the solutions of associated backward stochastic integral-partial differential equations driven by the observation process. In a heuristic way, their relations are explained, and the adjoint processes are expressed in terms of the adjoint vector fields, their gradients and Hessians, along the optimal state process. In this way the adjoint processes are naturally connected to the adjoint equation of the associated filtering equation. This shows that the conditional expectation in the maximum condition is computable through filtering the optimal state, as usually expected. Some variants of the partially observed stochastic maximum principle are derived, and the corresponding maximum conditions are quite different from the counterpart for the diffusion case. Finally, as an example, a quadratic optimal control problem with a free Poisson process and a Gaussian white-noised observation is explicitly solved using the partially observed maximum principle.
URI: http://hdl.handle.net/10397/19347
ISSN: 0095-4616
DOI: 10.1007/s00245-001-0031-9
Appears in Collections:Journal/Magazine Article

Access
View full-text via PolyU eLinks SFX Query
Show full item record

SCOPUSTM   
Citations

2
Last Week
0
Last month
0
Citations as of Aug 17, 2017

WEB OF SCIENCETM
Citations

3
Last Week
0
Last month
0
Citations as of Aug 12, 2017

Page view(s)

26
Last Week
1
Last month
Checked on Aug 13, 2017

Google ScholarTM

Check

Altmetric



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.