Note on the Relation between Compound and Composed Poisson Processes

I. In an article on such processes in ASTIN Bull. (11-3, pp. 45o-451) the author has derived a relation between cPp i.n.s. (compound Poisson processes in the narrow sense) and composed Poisson processes, which is quite general. In this note this relation shall be simplified under the rather weak condition that Po(0, Pro(t) being the distribution of the number of changes occurring in the interval (o, t), for every fixed value of t, tends to a positive limit less than unity when t tends to infinity.