42 citations · 70 across the 8 of their papers we have counts for
6 papers · 1 filter
Fractional Erlang Queues
Giacomo Ascione, Nikolai Leonenko, Enrica Pirozzi
We introduce a fractional generalization of the Erlang Queues . Such process is obtained through a time-change via inverse stable subordinator of the classical queue proce…
Limit theorems for filtered long-range dependent random fields
Tareq Alodat, Nikolai Leonenko, Andriy Olenko
This article investigates general scaling settings and limit distributions of functionals of filtered random fields. The filters are defined by the convolution of non-random kernel…
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…
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…
The multifaceted behavior of integrated supOU processes: The infinite variance case
Danijel Grahovac, Nikolai N. Leonenko, Murad S. Taqqu
The so-called "supOU" processes, namely the superpositions of Ornstein-Uhlenbeck type processes are stationary processes for which one can specify separately the marginal distribut…
Four moments theorems on Markov chaos
Solesne Bourguin, Simon Campese, Nikolai Leonenko +1
We obtain quantitative Four Moments Theorems establishing convergence of the laws of elements of a Markov chaos to a Pearson distribution, where the only assumption we make on the…