We study the superposition process of a class of independent renewal processes with longrange dependence. It is known that under two different scalings in time and space either fractional Brownian motion or a stable Lévy 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.
Publié le : 2003-08-14
Classification:
fractional Brownian motion,
heavy tails,
long-range dependence,
renewal processes,
weak convergence
@article{1066223274,
author = {Gaigalas, Raimundas and Kaj, Ingemar},
title = {Convergence of scaled renewal processes and a packet arrival model},
journal = {Bernoulli},
volume = {9},
number = {3},
year = {2003},
pages = { 671-703},
language = {en},
url = {http://dml.mathdoc.fr/item/1066223274}
}
Gaigalas, Raimundas; Kaj, Ingemar. Convergence of scaled renewal processes and a packet arrival model. Bernoulli, Tome 9 (2003) no. 3, pp. 671-703. http://gdmltest.u-ga.fr/item/1066223274/