Fractional non-homogeneous Poisson and Polya-Aeppli processes of order k and beyond

被引：3

作者：

Kadankova, Tetyana ^{[1
]}

Leonenko, Nikolai ^{[2
]}

Scalas, Enrico ^{[3
]}

机构：

[1] Vrije Univ Brussel, Dept Math, Brussels, Belgium

[2] Cardiff Univ, Sch Math, Cardiff, Wales

[3] Univ Sussex, Dept Math, Brighton, E Sussex, England

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2023年 / 52卷 / 08期

关键词：

non-homogeneous fractional Poisson process of order k non-homogeneous fractional Polya-Aeppli process of order k long range dependence; Caputo fractional derivative; alpha-stable Levy subordinators; fractional integro-differential difference equations;

D O I：

10.1080/03610926.2021.1958228

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We introduce two classes of point processes: a fractional non-homogeneous Poisson process of order k and a fractional non-homogeneous Polya-Aeppli process of order k. We characterize these processes by deriving their non-local governing equations. We further study the covariance structure of the processes and investigate the long-range dependence property.

引用

页码：2682 / 2701

页数：20

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