Abstract
Following a detailed discussion of the linear Kalman–Bucy filter for the l–dimensional case a description of Zakai nonlinear filtering of the n-dimensional logistic is presented. Explicit formulas for the c ∞-densities for least squares estimation of growth variables conditioned on continually updated community production or consumption records, are obtained. Application is made to a model of the myxomatosis disease in European wild rabbits and to a coral growth model with predation. Extensive use is made of the techniques of linear stochastic partial differential equations developed by H. Kunita, especially backward stochastic calculus and decomposition techniques
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