Mathematical Sciences: Topics in Heavy Tailed Modelling

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This is a three year program of research organized around the theme of heavy tailed modeling. Heavy tailed modeling assumes regular variation is present in either the right tail (frequently implying infinite variances) or the left tail of basic component distributions of the system and thus departs from Gaussian methods. Broad themes include parameter estimation and prediction in heavy tailed models (Hill estimator, linear programming estimator), model selection and confirmation and long range dependence. Specific classes of models to be studied are extreme value models, infinitely divisible processes and time series with positive innovations. Application areas include modeling financial and commodities markets and teletraffic systems. This is a three year program of research organized around two topics. The first involves modeling random phenomena whose behavior is controlled by exceedingly large values. For example, in communications, network performance can be dramatically affected by anomalous long calls such as computer logins by modem. Accurate modeling of these phenomena can lead to improvements in the system. The second topic deals with random phenomena in which dependencies in a system last a long time. Once again accurate modeling is important in improving system performance. Other applications of this research include modeling financial and commodities markets and modeling of water flows and heights.