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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-LN 2002-12
August 2002

Long Range Dependence, Heavy Tails and Rare Events


Gennady Samorodnitsky


These notes were prepared for a Concentrated Advanced Course at the University of Copenhagen in the framework of the MaPhySto program. The notes present an attempt to propose a new approach to long range dependence, one that is not mainly based on correlations, or on (approximate) self-similarity. Rather, we advocate a point of view that regards the passage between short memory and long memory and a phase transition in the way certain rare events happen. We are especially interested in the heavy tailed case. These notes bring together ideas from large deviations, theory of heavy tailed processes, extreme value theory and relate those to the notion of memory. Main examples considered are those related to communication networks and risk theory.

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