On the infinite divisibility of distributions of some inverse subordinators
Volume 5, Issue 4 (2018), pp. 509–519
Pub. online: 20 July 2018
Type: Research Article
Open Access
Open Access
Received
18 March 2018
18 March 2018
Revised
21 June 2018
21 June 2018
Accepted
29 June 2018
29 June 2018
Published
20 July 2018
20 July 2018
Abstract
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.
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