Mathematical Sciences: Extreme Values and Stochastic Models

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The various problems proposed fall in three categories, extreme value theory, point processes and time series. Sequences of extreme values or record times form a point process and hence the theory of point processes offers a powerful tool to analyze the related problems. The principal investigator has a number of results in this area and will continue his investigation further. The point processes methods that proved to be so useful in showing the convergence of functionals of moving average processes will be extended to the continuous time processes. New point processes methods need to be developed since the random points generated in many relevant situations have a very complicated dependence structure. The ideas of convex hulls of a set of points lead to one possible way of defining multivariate extremes. Thus the multivariate order statistics depend on the distribution theory of the convex hulls.