Decoupling Moment Equations for Stochastic Population Models

Abstract

Stochastic population models incorporating realistic transition probabilities may result in an open coupled system of differential equations for the moments which cannot be solved successively and must be decoupled in order to obtain estimates for the moments. Three existing general techniques are reviewed each of which reduces the coupled system to a set of nonlinear equations which may be solved using a numerical integration method. For the case where only estimates of the first 2 moments are required 2 existing techniques are presented and a new technique is developed and in each case the use of a numerical integration method is avoided. All of the techniques are compared for a stochastic model of a chemical process and the new technique performs favorably. A second example related to the logistic model of growth reveals a problem with one of the existing techniques and provides an insight into problems with stochastic models which have mean logistic behavior.