Statistical and Applied Mathematical Sciences Institute
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Research Triangle Park, NC 27709-4006
Tel: 919.685.9350 FAX: 919.685.9360
info@samsi.info

SAMSI course on 

"Long-range Dependence and Heavy Tails"

Network Modeling for the Internet Program

Instructor:  Professor Murad S. Taqqu, SAMSI, University of North Carolina & Boston University

Class Time:  Thursdays, 4:30 - 7:00pm

Class Location:  NISS Building, Room 104

Class begins September 4, 2003

University Listings

Duke University    STA 293.03

UNC-CH              STAT 322

NC State               ST 810U-006

Course Description

This course will focus on long-range dependence and heavy tails, notions which are relevant in computer traffic networks. Long-range dependence occurs when the covariances of a time series decrease slowly, like a power function. Heavy tails occur when the probability distribution of the time series has infinite variance and behaves like a power function. We will introduce self-similar processes which are idealized models that can encompass long-range dependence and/or heavy tails. We will focus first on fractional Brownian motion and on the related FARIMA time series models. To deal with infinite variance and heavy tails, we will introduce in a systematic fashion, infinite variance stable processes. We will study their properties and describe a number of stable (heavy-tailed) self-similar processes, including the so-called "Telecom model". We will also describe statistical methods for detecting the presence of long-range dependence and for estimating its intensity, focusing on wavelet methods since these are particularly useful in this regard.

Prerequisites:    One year of probability and statistics, preferably at the graduate level.

Required Text:

"Theory and Applications of Long-range Dependence". Paul Doukhan, Georges Oppenheim and Murad S. Taqqu editors. ISBN 0-8176-4168-8. Birkhauser, Boston (2003).

Optional Texts:

"Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance". Gennady Samorodnitsky and Murad S. Taqqu, ISBN 0-412-05171-0, Chapman and Hall/CRC, New York (1994).

"Selfsimilar processes". Paul Embrechts and Mokoto Maejima, ISBN 0-691-096627-9 Princeton University Press (2003).

Lecture Note 1

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