Bounds for the total variation distance between the distribution of the sum of a random number of Bernoulli summands and an appropriate Poisson distribution are given. The results can be used to derive limit theorems with rates of convergence for marked and thinned point processes. Some examples...

A characterization of Cox and renewal processes which concerns thinning is given. It is shown that all the possible original processes of a given Cox and renewal process are thinnings of other renewal processes, for every thinning parameter p [epsilon] (0, 1).