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Finite thinning-selfdecomposable point processes

Journal article
Authors Michel Davydov
Sergei Zuyev
Published in Statistics and Probability Letters
Volume 146
Pages 132-138
ISSN 01677152
Publication year 2019
Published at Department of Mathematical Sciences
Pages 132-138
Language en
Keywords Cluster process, Limit theorems, Point process, Selfdecomposability, Superposition scheme, Thinning
Subject categories Mathematics

Abstract

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.

Page Manager: Webmaster|Last update: 9/11/2012
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