Nonlinear filtering of a system of logistic equations

Abstract

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.