Non-homogeneous space-time fractional Poisson processes

被引:4
|
作者
Maheshwari, A. [1 ]
Vellaisamy, P. [2 ]
机构
[1] Indian Inst Management Indore, Operat Management & Quantitat Tech, Rau Pithampur Rd, Indore 453556, Madhya Pradesh, India
[2] Indian Inst Technol, Dept Math, Mumbai, Maharashtra, India
关键词
Levy subordinator; fractional Poisson process; non-homogeneous Poisson process; LIMIT-THEOREMS; FIELDS;
D O I
10.1080/07362994.2018.1541749
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The space-time fractional Poisson process (STFPP), defined by Orsingher and Poilto (2012), is a generalization of the time fractional Poisson process (TFPP) and the space fractional Poisson process (SFPP). We study the fractional generalization of the non-homogeneous Poisson process and call it the non-homogeneous space-time fractional Poisson process (NHSTFPP). We compute their pmf and generating function and investigate the associated differential equation. The limit theorems for the NHSTFPP process are studied. We study the distributional properties, the asymptotic expansion of the correlation function of the non-homogeneous time fractional Poisson process (NHTFPP) and subsequently investigate the long-range dependence (LRD) property of a special NHTFPP. We investigate the limit theorem for the fractional non-homogeneous Poisson process (FNHPP) studied by Leonenko etal. (2014). Finally, we present some simulated sample paths of the NHSTFPP process.
引用
收藏
页码:137 / 154
页数:18
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