Skip to Main content Skip to Navigation
Journal articles

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

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. Such processes bear some analogy with L'evy processes, but are more complex since their increments are neither stationary nor independent. In [3], the Hausdorf multifractal spectrum of these processes were computed. We are interested here in their Large Deviation and Legendre multifractal spectra. These "statistical" spectra are seen to give, in this case, a richer information than the "geometrical" Hausdorf spectrum. In addition, our results provide a firm theoretical basis for the empirical discovery of the multifractal nature of TCP traffic.
Document type :
Journal articles
Complete list of metadata

Cited literature [27 references]  Display  Hide  Download

https://hal.inria.fr/inria-00633195
Contributor : Lisandro Fermin <>
Submitted on : Monday, October 22, 2012 - 4:02:47 PM
Last modification on : Monday, November 23, 2020 - 12:52:03 PM
Long-term archiving on: : Wednesday, January 23, 2013 - 3:43:15 AM

File

v12.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Jacques Lévy Véhel, Michal Rams. Large Deviation Multifractal Analysis of a Class of Additive Processes with Correlated Non-Stationary Increments. IEEE/ACM Transactions on Networking, IEEE/ACM, 2013, 21 (4), pp.1309-1321. ⟨10.1109/tnet.2012.2229469⟩. ⟨inria-00633195v2⟩

Share

Metrics

Record views

447

Files downloads

626