Superposition of Diffusions with Linear Generator and its Multifractal Limit Process

Endre Iglói; György Terdik

ESAIM: Probability and Statistics (2010)

  • Volume: 7, page 23-88
  • ISSN: 1292-8100

Abstract

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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.


How to cite

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Iglói, Endre, and Terdik, György. "Superposition of Diffusions with Linear Generator and its Multifractal Limit Process." ESAIM: Probability and Statistics 7 (2010): 23-88. <http://eudml.org/doc/104307>.

@article{Iglói2010,
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.
},
author = {Iglói, Endre, Terdik, György},
journal = {ESAIM: Probability and Statistics},
keywords = {Fractals; long range dependence; self-similarity; stationarity; higher order statistics; bispectrum; network traffic; superposition; diffusion processes; CIR process; DLG process; square root process.; fractals; higher order statistics; CIR processes; square root process},
language = {eng},
month = {3},
pages = {23-88},
publisher = {EDP Sciences},
title = {Superposition of Diffusions with Linear Generator and its Multifractal Limit Process},
url = {http://eudml.org/doc/104307},
volume = {7},
year = {2010},
}

TY - JOUR
AU - Iglói, Endre
AU - Terdik, György
TI - Superposition of Diffusions with Linear Generator and its Multifractal Limit Process
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 7
SP - 23
EP - 88
AB - 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.

LA - eng
KW - Fractals; long range dependence; self-similarity; stationarity; higher order statistics; bispectrum; network traffic; superposition; diffusion processes; CIR process; DLG process; square root process.; fractals; higher order statistics; CIR processes; square root process
UR - http://eudml.org/doc/104307
ER -

References

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