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Superposition of Diffusions with Linear Generator and its Multifractal Limit Process

Published online by Cambridge University Press:  15 May 2003

Endre Iglói  and
György Terdik
Endre Iglói
Affiliation:
Institute of Mathematics and Informatics, University of Debrecen, 4010 Debrecen, PF 12, Hungary; terdik@cic.unideb.hu.
György Terdik
Affiliation:
Institute of Mathematics and Informatics, University of Debrecen, 4010 Debrecen, PF 12, Hungary; terdik@cic.unideb.hu.
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Abstract

In this paper a new multifractal stochastic process called Limit of theIntegrated Superposition of Diffusion processes with Linear differencialGenerator (LISDLG) is presented which realistically characterizes the networktraffic multifractality. Several properties of the LISDLG model are presentedincluding long range dependence, cumulants, logarithm of the characteristicfunction, dilative stability, spectrum and bispectrum. The model captureshigher-order statistics by the cumulants. The relevance and validation of theproposed model are demonstrated by real data of Internet traffic.


Keywords

Fractalslong range dependenceself-similaritystationarityhigher orderstatisticsbispectrumnetwork trafficsuperpositiondiffusion processesCIR processDLG processsquare root process.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 7 , March 2003 , pp. 23 - 88
Copyright
© EDP Sciences, SMAI, 2003

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