My present main interest is
mathematical and statistical theory for Extreme Episodes in random
processes, and to use the theory to solve practical problems. It
revolves around two mathematical themes: High-dimensional and detailed
statistical models and methods for extreme episodes; and the “shape” of
extreme episodes in non-differentiable Gaussian processes. Science and
technology are producing enormously large data sets, at an ever
increasing rate. These data sets are ready to be used for scientific
discovery and technological advance, in ways beyond present
imagination. The theory of extreme episodes will be one part of the
answer to this challenge, I believe – what is needed is a much more
sophisticated understanding of extreme behavior than what is given by
existing theory. The results will aid efforts to mitigate the impact of
the extreme floods, windstorms, and heat waves which might be caused by
a changing climate. They will lead to improved methods
to avoid both fatal and less serious car accidents, and they will be
used to diminish financial risks. Additional interests of mine are
discrete hedging and credit risk.
