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.

Point process

Limit theorems


Cluster process


Superposition scheme


Michel Davydov

Ecole Normale Superieure de Cachan

Sergey Zuev

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Statistics and Probability Letters

0167-7152 (ISSN)

Vol. 146 132-138

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Mathematical Analysis



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