Fractional Poisson Fields and Martingales
Probability
2018-01-30 v4 Statistics Theory
Statistics Theory
Abstract
We present new properties for the Fractional Poisson process and the Fractional Poisson field on the plane. A martingale characterization for Fractional Poisson processes is given. We extend this result to Fractional Poisson fields, obtaining some other characterizations. The fractional differential equations are studied. We consider a more general Mixed-Fractional Poisson process and show that this process is the stochastic solution of a system of fractional differential-difference equations. Finally, we give some simulations of the Fractional Poisson field on the plane.
Cite
@article{arxiv.1601.08136,
title = {Fractional Poisson Fields and Martingales},
author = {Giacomo Aletti and Nikolai Leonenko and Ely Merzbach},
journal= {arXiv preprint arXiv:1601.08136},
year = {2018}
}