Stochastic models of grouping changes

Abstract

Several simple stochastic models are given for a finite closed system of individuals existing in clusters which may come together to form larger clusters which may in turn split up. Some of these models are analysed and compared in equilibrium. Several of the models fit into a general framework established and investigated by Whittle (1965a); it is shown that these models have an equilibrium solution of a particularly simple form, deduced by Whittle, if and only if the models are stochastically reversible. A normal approximation to two of the models in equilibrium is found to give the same mean value as a deterministic approximation.