A stochastic Gompertz model with hereditary effect.

In this paper we have studied a stochastic version of the Gompertz model for population growth of a single species after incorporating the aspect of heredity. Various statistical characteristics--the mean-value function, covariance-kernel, etc.--are evaluated for a delta-correlated process and their asymptotic values obtained. The effect of the hereditary kernel on the various statistics is discussed and it is found that it is to shift the distribution towards the origin.