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Multifractal Analysis of a Class of Additive Processes with Correlated Non-Stationary Increments

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1.	Title	Title of document	Multifractal Analysis of a Class of Additive Processes with Correlated Non-Stationary Increments
2.	Creator	Author's name, affiliation, country	Julien Barral; INRIA Rocquencourt, France
2.	Creator	Author's name, affiliation, country	Jacques Lévy Véhel; NRIA Rocquencourt, France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)
4.	Description	Abstract	We consider a family of stochastic processes built from infinite sums of independent positive random functions on $R_+$. Each of these functions increases linearly between two consecutive negative jumps, with the jump points following a Poisson point process on $R_+$. The motivation for studying these processes stems from the fact that they constitute simplified models for TCP traffic on the Internet. Such processes bear some analogy with Lévy processes, but they are more complex in the sense that their increments are neither stationary nor independent. Nevertheless, we show that their multifractal behavior is very much the same as that of certain Lévy processes. More precisely, we compute the Hausdorff multifractal spectrum of our processes, and find that it shares the shape of the spectrum of a typical Lévy process. This result yields a theoretical basis to the empirical discovery of the multifractal nature of TCP traffic.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2004-06-09
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/208
10.	Identifier	Digital Object Identifier	10.1214/EJP.v9-208
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 9
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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