Correlated fluctuations in multielement systems: The stochastic-branching-process model.

Abstract

A problem of correlated fluctuations in multielement systems is considered in the framework of the theory of stochastic branching processes and is formulated in terms of a population model. Correlations have been taken into account by means of the heredity function. An explicit mathematical method is proposed to solve the problem without referring to the complicated theory of general branching processes. Using this method the global statistical properties of the system (e.g., the ensemble average and the probability of extinction) have been found. Possible applications of the present model are discussed.