We consider a stochastic model for the spread of an epidemic among a population of n individuals that are equally spaced around a circle. Throughout its infectious period, a typical infective, i say, makes global contacts, with individuals chosen independently and uniformly from the whole...

This paper is concerned with the approximation of early stages of epidemic processes by branching processes. A general model for an epidemic in a closed, homogeneously mixing population is presented. A construction of a sequence of such epidemics, indexed by the initial number of susceptibles N,...

It is shown that the distribution of the number of ones in the binary expansion of an integer chosen uniformly at random from the set 0, 1,..., n - 1 can be approximated in total variation by a mixture of two neighbouring binomial distributions, with error of order (log n)-1. The proof uses...

In contrast to the classical theory of partial sums of independent and identically distributed random variables, the maximum value taken by a component of a Markov population process xN is typically largely determined by the variation in its mean, rather than by stochastic fluctuation. A closer...

Poisson approximation in total variation can be successfully established in a wide variety of contexts, involving sums of weakly dependent random variables which usually take the value 0, and occasionally the value 1. If the random variables can take other positive integer values, or if there is...

The Stein-Chen method for Poisson approximation is adapted into a form suitable for obtaining error estimates for the approximation of the whole distribution of a point process on a suitable topological space by that of a Poisson process. The adaptation involves consideration of an...