Branching particle systems and compound Poisson processes related to Pólya-Aeppli distributions

Branching Particle Systems and Compound Poisson Processes Related to Pólya-aeppli Distributions

We establish numerous new refined local limit theorems for a class of compound Poisson processes with Pólya-Aeppli marginals, and for a particular family of the branching particle systems which undergo critical binary branching and can be approximated by the backshifted Feller diffusion. To this end, we also derive new results for the families of Pólya–Aeppli and Poisson–exponential distributio...

Proof of logconcavity of some compound Poisson and related distributions

Compound Poisson distributions play important role in many applications (telecommunication, hydrology, insurance, etc.). In this paper, we prove that some of the compound Poisson distributions have the logconcavity property that makes them applicable in stochastic programming problems. The proofs are based on classical Turan types theorem and orthogonal polynomials. Acknowledgements: Please ins...

Fractional Processes: from Poisson to Branching One

Fractional generalizations of the Poisson process and branching Furry process are considered. The link between characteristics of the processes, fractional differential equations and Lèvy stable densities are discussed and used for construction of the Monte Carlo algorithm for simulation of random waiting times in fractional processes. Numerical calculations are performed and limit distribution...

Poisson processes , ordinary and compound

The Poisson process is a stochastic counting process that arises naturally in a large variety of daily-life situations. We present a few definitions of the Poisson process and discuss several properties as well as relations to some well-known probability distributions. We further briefly discuss the compound Poisson process.

Poisson processes (and mixture distributions)