The fractional non-homogeneous Poisson process

被引：26

作者：

Leonenko, Nikolai ^{[1
]}

Scalas, Enrico ^{[2
]}

Trinh, Mailan ^{[2
]}

机构：

[1] Cardiff Univ, Sch Math, Senghennydd Rd, Cardiff CF24 4AG, S Glam, Wales

[2] Univ Sussex, Dept Math, Sch Math & Phys Sci, Brighton BN1 9QH, E Sussex, England

来源：

STATISTICS & PROBABILITY LETTERS | 2017年 / 120卷

基金：

澳大利亚研究理事会;

关键词：

Fractional point processes; Levy processes; Time-change; Subordination;

D O I：

10.1016/j.spl.2016.09.024

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 a non-homogeneous fractional Poisson process by replacing the time variable in the fractional Poisson process of renewal type with an appropriate function of time. We characterize the resulting process by deriving its non-local governing equation. We further compute the first and second moments of the process. Eventually, we derive the distribution of arrival times. Constant reference is made to previous known results in the homogeneous case and to how they can be derived from the specialization of the non homogeneous process. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：147 / 156

页数：10

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