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Issue ESAIM: P&S Volume 7, 2003 Page(s) 23 - 88 DOI 10.1051/ps:2003008

ESAIM: P&S, March 2003, Vol. 7, pp. 23-88
DOI: 10.1051/ps:2003008

Superposition of Diffusions with Linear Generator and its Multifractal Limit Process

Endre Iglói and György Terdik

Institute of Mathematics and Informatics, University of Debrecen, 4010 Debrecen, PF 12, Hungary; terdik@cic.unideb.hu.

(Received May 14, 2002.)

Abstract
In this paper a new multifractal stochastic process called Limit of the Integrated Superposition of Diffusion processes with Linear differencial Generator (LISDLG) is presented which realistically characterizes the network traffic multifractality. Several properties of the LISDLG model are presented including long range dependence, cumulants, logarithm of the characteristic function, dilative stability, spectrum and bispectrum. The model captures higher-order statistics by the cumulants. The relevance and validation of the proposed model are demonstrated by real data of Internet traffic.

Mathematics Subject Classification. 62M10, 60J60, 60G10, 93E12

Key words: Fractals, long range dependence, self-similarity, stationarity, higher order statistics, bispectrum, network traffic, superposition, diffusion processes, CIR process, DLG process, square root process.


© EDP Sciences, SMAI 2003

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