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.