Cardiff University
School of Mathematics
Statistics and OR Seminar
Professor Gyorgy Terdik, University of Debrecen,
HUNGARY
Superposition of Diffusions with Linear
Generator and its Multifractal Limit Process.
A Working Model for High-Speed Network Data
Computer network traffic has recently been the subject of various types of
statistical studies including fractal analysis, and in particular, measuring
and modeling Long-Range Dependence (LRD), investigating self-similarity,
and showing multifractal properties. The common agreement among
several empirical findings about the general properties of traces is
summarized in as follows.
· Many signals show significant LRD, but behavior inconsistent with strict
self-similarity.
· For many signals, the scaling behavior of moments as the signal is
aggregated is a nontrivial function of the moment order.
· Many signals have increments that are inherently positive, skewed and
hence non-Gaussian.
There are some additional properties motivated by our experimental study
of ATM traces, providing strong evidence of the presence of Gamma
distribution and real-valued bispectrum. Therefore there are two
additional requirements.
· The marginal distribution of signals of ATM traces is close to Gamma
distribution.
· Signals of ATM traces have a real-valued bispectrum.
Having these properties in mind we have studied a certain nonlinear
diffusion process, superposition of such processes with random coefficients,
the limit of the centralized integral processes of the superposition processes
and its increment process. The main objective is to find a multifractal
model which has an analytically and statistically tractable higher order
cumulant structure.
We have applied our model to real data. The time series of ATM traces
measured in SUNET fits our model very well. The feasibility
of carrying out parameter estimation utilizing the dilative stability is also
discussed to some extent.
14.00 Wednesday, JULY 30, 2003, Room M/0.37
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