Convergence of scaled renewal processes and a packet arrival model

被引：43

作者：

Gaigalas, R ^{[1
]}

Kaj, I ^{[1
]}

机构：

[1] Uppsala Univ, Dept Math, S-75106 Uppsala, Sweden

来源：

BERNOULLI | 2003年 / 9卷 / 04期

关键词：

fractional Brownian motion; heavy tails; long-range dependence; renewal processes; weak convergence;

D O I：

10.3150/bj/1066223274

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 study the superposition process of a class of independent renewal processes with long-range dependence. It is known that under two different scalings in time and space either fractional Brownian motion or a stable Levy process may arise in the rescaling asymptotic limit. It is shown here that in a third, intermediate scaling regime a new limit process appears, which is neither Gaussian nor stable. The new limit process is characterized by its cumulant generating function and some of its properties are discussed.

引用

页码：671 / 703

页数：33

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