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arXiv · 1803.06702

On the infinite divisibility of distributions of some inverse subordinators

Arun Kumar·Erkan Nane
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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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Arun Kumar, Erkan Nane. 2018-03-18. On the infinite divisibility of distributions of some inverse subordinators. https://doi.org/10.15559/18-vmsta108

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