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math.PR2018
Tempered Fractional Poisson Processes and Fractional Equations with Z-Transform
Neha Gupta, Arun Kumar, Nikolai Leonenko
In this article, we derive the state probabilities of different type of space- and time-fractional Poisson processes using z-transform. We work on tempered versions of time-fractio…
math.ST2018
Fractional Risk Process in Insurance
Arun Kumar, Nikolai Leonenko, Alois Pichler
Important models in insurance, for example the Carm{é}r--Lundberg theory and the Sparre Andersen model, essentially rely on the Poisson process. The process is used to model arriva…
math.PR2018
On the infinite divisibility of distributions of some inverse subordinators
Arun Kumar, Erkan Nane
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 inve…