分数负二项和Pólya过程

IF 0.4 4区数学 Q4 STATISTICS & PROBABILITY

Probability and Mathematical Statistics-Poland Pub Date : 2013-06-11 DOI:10.19195/0208-4147.38.1.5

P. Vellaisamy, A. Maheshwari

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引用次数: 18

摘要

在负二项过程的gamma从属形式中，我们用分数阶泊松过程FPP代替分数阶泊松过程，定义了分数阶负二项过程FNBP。证明了FPP和FNBP的一维分布不是无限可分的。此外，空间分数阶Pólya过程SFPP是通过在空间分数阶泊松过程的定义中用gamma随机变量替换速率参数λ来定义的。研究了FNBP和SFPP的性质以及与pde的关系对FNBP和SFPP密度的影响。

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Fractional negative binomial and Pólya processes

In this paper, we define a fractional negative binomial process FNBP by replacing the Poisson process by a fractional Poisson process FPP in the gamma subordinated form of the negative binomial process. It is shown that the one-dimensional distributions of the FPP and the FNBP are not infinitely divisible. Also, the space fractional Pólya process SFPP is defined by replacing the rate parameter λ by a gamma random variable in the definition of the space fractional Poisson process. The properties of the FNBP and the SFPP and the connections to PDEs governing the density of the FNBP and the SFPP are also investigated.

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来源期刊

Probability and Mathematical Statistics-Poland STATISTICS & PROBABILITY-

CiteScore

0.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： PROBABILITY AND MATHEMATICAL STATISTICS is published by the Kazimierz Urbanik Center for Probability and Mathematical Statistics, and is sponsored jointly by the Faculty of Mathematics and Computer Science of University of Wrocław and the Faculty of Pure and Applied Mathematics of Wrocław University of Science and Technology. The purpose of the journal is to publish original contributions to the theory of probability and mathematical statistics.