Time development of a Markov process in a finite population: Application to diffusion of information

A systematic procedure of truncating the hierarchy of moment equations describing the stochastic evolution of a Markov process in a finite population is developed. The procedure makes use of the asymptotic expression for a certain higher‐order moment of the relevant probability distribution and yields finite‐size corrections to all lower‐order moments. The usefulness of the method is illustrated by applying it to study the mean and the variance of the stochastic variable n(t), the number of active spreaders at time t, in Bartholomew's model of diffusion of information. The results thus obtained are compared with the ones following from the exact probability distribution for the model (wherever known) and the agreement between the two sets of results is found to be remarkably good.