On the Use of the Normal Approximation in the Treatment of Stochastic Processes

Abstract

Summary A method of treating nonlinear Markov processes is discussed, based on the assumption that the variates are normally distributed. The method is applied to models of logistic population growth, plant competition, and animal predation. In the preparatory section (§2) an alternative form (9) of the Bartlett relation is deduced, which is relatively convenient if one wishes to derive equations for the cumulants of a Markov process; the relation is particularly useful in the case of normal processes. In order that one may treat the joint distribution of the variate values at several instants of time, the Bartlett relation is generalized to provide equations (40) and (41) for the characteristic functional of the process. The validity of the “normalization technique” is discussed in the final section, and a comparison made with other methods.