The Fractional Poisson Process and the Inverse Stable Subordinator
The Fractional Poisson Process and the Inverse Stable Subordinator
The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a Poisson process. This paper shows that a traditional Poisson process, with the time variable replaced by an independent inverse stable subordinator, is also a fractional …