On the Long-Range Dependence of Mixed Fractional Poisson Process

TL;DR

This paper demonstrates that the mixed fractional Poisson process exhibits long-range dependence, while its increments, the mixed fractional Poissonian noise, show short-range dependence, contributing to understanding their dependence structures.

Contribution

It establishes the LRD property of the MFPP and the SRD property of its increments, providing new insights into their dependence characteristics.

Findings

MFPP exhibits long-range dependence.

Increments of MFPP (MFPN) have short-range dependence.

Asymptotic covariance results support the dependence properties.

Abstract

In this paper, we show that the mixed fractional Poisson process (MFPP) exhibits the long-range dependence (LRD) property. It is proved by establishing an asymptotic result for the covariance of inverse mixed stable subordinator. Also, it is shown that the increments of the MFPP, namely, the mixed fractional Poissonian noise (MFPN) has the short-range dependence (SRD) property.