Author
E. Orsingher
Bio: E. Orsingher is an academic researcher. The author has contributed to research in topics: Poisson distribution & Subordinator. The author has an hindex of 1, co-authored 1 publications receiving 1 citations.
Topics: Poisson distribution, Subordinator
Papers
More filters
Posted Content•
TL;DR: In this paper, the authors studied some extensions of the Poisson process of order $i$ for different forms of weights and also with the time-changed versions, with Bern\v stein subordinator playing the role of time.
Abstract: The Poisson process of order $i$ is a weighted sum of independent Poisson processes and is used to model the flow of clients in different services. In the paper below we study some extensions of this process, for different forms of the weights and also with the time-changed versions, with Bern\v stein subordinator playing the role of time. We focus on the analysis of hitting times of these processes obtaining sometimes explicit distributions. Since all the processes examined display a similar structure with multiple upward jumps sometimes they can skip all states with positive probability even on infinitely long time span.
1 citations
Cited by
More filters
01 Jan 2021
TL;DR: In this paper, the authors present recent results on the fractional versions of point processes and discuss generalization attempted by several authors in this direction, and present some plots and simulations of the well-known fractional Poisson process of Laskin (2003).
Abstract: In the last two decades, the theoretical advancement of the point processes witnessed an important and deep interconnection with the fractional calculus. It was also found that the stable subordinator plays a vital role in this connection. The survey intends to present recent results on the fractional versions of point processes. We will also discuss generalization attempted by several authors in this direction. Finally, we present some plots and simulations of the well-known fractional Poisson process of Laskin (2003).