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Nonlinear filtering of a system of logistic equations

Published online by Cambridge University Press:  17 April 2009

Rehez Ahlip  and
Vo Anh
Rehez Ahlip
Affiliation:
Department of Mathematics and Statistics, University of Western Sydney, Macarthur, Campbelltown NSW 2560, Australia e-mail: r.ahlip@ums.edu.au
Vo Anh
Affiliation:
School of Mathematics, Queensland University of Technology, GPO Box 2434, Brisbane Qld 4001, Australia e-mail: v.anh@fsc.qut.edu.au
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This paper is concerned with the filtering problem for a nonlinear stochastic system of prey-predator logistic equations. Based on the innovations approach, we establish the Zakai equation for the unnormalised conditional distribution and the adjoint Zakai equation for the unnormalised conditional density of the nonlinear filter. Using a perturbation technique, we obtain the appropriate expressions for the unnormalised conditional distribution and density of stochastic integrals with respect to the observation processes.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 55 , Issue 2 , April 1997 , pp. 219 - 238
Copyright
Copyright © Australian Mathematical Society 1997

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