Finite thinning-selfdecomposable point processes

Journal article, 2019

Thinning-selfdecomposable point processes arise as a limit in the thinning-superposition schemes of independent but not necessarily identically distributed point processes and, as such, they constitute a strict subclass of infinitely divisible point processes. At the same time they are strictly larger than the class of discrete α-stable point processes which are the limits of a scaled superposition of independent identically distributed processes. We give a series representation for finite thinning-selfdecomposable point processes which can be viewed as an analogue of an integral representation of selfdecomposable (or class L) random variables.