ISSN:
1573-2878
Keywords:
Nonlinear filtering
;
likelihood ratio
;
parameter identification
;
optimal control
;
distributed-parameter systems
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00939904
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