On the infinite divisibility of distributions of some inverse subordinators - Arun Kumar; Erkan Nane (Modern Stochastics: Theory and Applications, 2018)
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.