Author:
Leonenko Nikolai,Scalas Enrico,Trinh Mailan
Abstract
AbstractThe fractional nonhomogeneous Poisson process was introduced by a time change of the nonhomogeneous Poisson process with the inverseα-stable subordinator. We propose a similar definition for the (nonhomogeneous) fractional compound Poisson process. We give both finite-dimensional and functional limit theorems for the fractional nonhomogeneous Poisson process and the fractional compound Poisson process. The results are derived by using martingale methods, regular variation properties and Anscombe’s theorem. Eventually, some of the limit results are verified in a Monte Carlo simulation.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Cited by
6 articles.
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