On the infinite divisibility of distributions of some inverse subordinators

Modern Stochastics: Theory and Applications

卷:5

Erkan Nane¹  Arun Kumar² 

[1] Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, USA;

[2] Department of Mathematics, Indian Institute of Technology Ropar, Punjab 140001, India;

关键词: Infinite divisibility;    subordinators;    inverse subordinators;    fractional Poisson process;   

DOI  :  10.15559/18-VMSTA108

来源: DOAJ

【 摘 要 】

We consider the infinite divisibility of distributions of some well-known inverse subordinators. Using a tail probability bound, we establish that distributions of many of the inverse subordinators used in the literature are not infinitely divisible. We further show that the distribution of a renewal process time-changed by an inverse stable subordinator is not infinitely divisible, which in particular implies that the distribution of the fractional Poisson process is not infinitely divisible.

【 授权许可】

Unknown