Theory and Applications of Heavy Tails and Long Range Dependence

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The PIs propose a new approach to thinking about long range dependence by means of phase transitions, which extends typical thinking in terms of product moments which exist unreliably. Such an approach will likely lead to new directions of research, for example to new connections between probability theory and ergodic theory. Furthermore, various difficult issues concerning heavy tails will be investigated, including high dimension problems, visualization problems, impact of minimum distance methodology and asymptotic sufficiency. Application areas include financial engineering, data networks, hydrology, meteorology and environmental studies, risk analysis. A three year program of research by Sidney Resnick and Gennady Samorodnitsky will deal with theoretical and practical problems about phenomena with heavy tails and/or long range dependence. Long range dependence is a property of a model in which dependence persists over exceptionally long time periods. Heavy tails are exhibited by model subject to particularly large shocks. Both notions are practically important (in internet modeling, finance, reliability ) and theoretically challenging.