Superposition of diffusions with linear generator and its multifractal limit process
ESAIM: Probability and Statistics, Tome 7 (2003), pp. 23-88.

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.

DOI : 10.1051/ps:2003008
Classification : 62M10, 60J60, 60G10, 93E12
Mots-clés : fractals, long range dependence, self-similarity, stationarity, higher order statistics, bispectrum, network traffic, superposition, diffusion processes, CIR process, DLG process, square root process 
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     author = {Igl\'oi, End and Terdik, Gy\"orgy},
     title = {Superposition of diffusions with linear generator and its multifractal limit process},
     journal = {ESAIM: Probability and Statistics},
     pages = {23--88},
     publisher = {EDP-Sciences},
     volume = {7},
     year = {2003},
     doi = {10.1051/ps:2003008},
     mrnumber = {1956073},
     zbl = {1017.60087},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ps:2003008/}
}
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Iglói, End; Terdik, György. Superposition of diffusions with linear generator and its multifractal limit process. ESAIM: Probability and Statistics, Tome 7 (2003), pp. 23-88. doi : 10.1051/ps:2003008. http://www.numdam.org/articles/10.1051/ps:2003008/

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