Parameter identification for partially observed diffusions
Date
1992Source Title
Journal of Optimization Theory and Applications
Print ISSN
223239
Publisher
Kluwer Academic Publishers-Plenum Publishers
Volume
75
Issue
1
Pages
33 - 50
Language
English
Type
ArticleItem Usage Stats
212
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221
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Abstract
In this paper, we consider the identification problem of drift and dispersion parameters for a class of partially observed systems governed by Ito equations. Using the pathwise description of the Zakai equation, we formulate the original identification problem as a deterministic control problem in which the unnormalized conditional density (solution of the Zakai equation) is treated as the state, the unknown parameters as controls, and the likelihood ratio as the objective functional. The question of existence of elements in the parameter set that maximize the likelihood ratio is discussed. Further, using variational arguments and the Gateaux differentiability of the unnormalized density on the parameter set, we obtain the necessary conditions for optimal identification. © 1992 Plenum Publishing Corporation.
Keywords
distributed-parameter systemslikelihood ratio
Nonlinear filtering
optimal control
parameter identification
Differentiation (calculus)
Diffusion
Distributed parameter control systems
Mathematical models
Optimal control systems
Signal filtering and prediction
State space methods
Variational techniques
Deterministic control problem
Gateaux differentiability
Ito equations
Likelihood ratio
Nonlinear filtering
Optimal control
Parameter identification
Zakai equation
Parameter estimation
Permalink
http://hdl.handle.net/11693/26100Published Version (Please cite this version)
http://dx.doi.org/10.1007/BF00939904Collections
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