Topics in Heavy Tailed Modeling and Long Range Dependence

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9704982 Resnick Sidney Resnick and Gennady Samorodnitsky will continue a program of research organized around the theme of heavy tailed modeling and its connections to long range dependence. Heavy tailed modeling frequently implies infinite variances and thus departs from Gaussian methods. Broad themes of the research program include parameter estimation and prediction in heavy tailed models, model selection and confirmation, and the interplay between long range dependence and heavy tails. Special attention is given to application areas which include the financial and commodities markets and teletraffic networks such as the World Wide Web. Both probabilistic modeling and statistical issues are emphasized. Statistical issues include coping with changes of methods implied by non-standard data features such as long range dependence, lack of existence of moments and correlations, and dependencies which cannot be captured by linear structures. Probabilistic models will be formulated and studied in an attempt to qualitatively explain observed features of the data. The increasing instrumentation of both financial markets and broadband data networks makes possible the collection of huge quantities of data. Examination of some of the data reveals features that classical statistics and probability models are not used to dealing with and hence, this project has a dual purpose: (a) To develop statistical tools which use the data to more reliably fit models and make predictions; (b) To build probability models which provide qualitative insights into the nature of the system under investigation. For example, modern broadband networks exhibit characteristics much different from what is predicted by classical models. A question which may be answered by this research is, "when is it economically advisable to add service capacity to the network?".