ABSTRACT
A. J. Lotka and V. Volterra initiated independently the deterministic theory of population dynamics. The stochastic theory of population dynamics was initiated by Feller almost forty years ago. Since then a vast amount of works dealing with stochastic models for population studies has appeared. The justification for such stochastic models can be found in the books by Bartlett, Iosifescu and Tautu, May, and Goel and Richter-Dyn. This chapter presents a survey of various stochastic models of interacting populations in a prey-predator relationship. The earliest stochastic model of interacting populations in a prey-predator relationship is probably due to Chiang and is based on birth and death processes. Several authors have considered the special case of prey-predator interaction in which one population influences the growth of the other without being itself influenced by the other. Georges A. Becus used the formalism and results of the theory of random evolutions to study the Gompertzian model.
