The investigator proposes to study three problems which pertain to the extremal theory for stationary stochastic processes. The first problem involves the statistical inference of a quantity called the extremal index, which is of importance to the statistical theory of extremes of dependent data. The second problem involves the study of properties of a two- dimensional random measure which records the excursions of high levels by a continuous-time stationary process. The third topic involves the extremes of a shot noise process. Applications to results will be considered. This investigator works in the field of probability, in the area of extreme value theory. He proposes to study three topics which have been studied by many other researchers in this area. A successful completion of any of these projects will have positive impact on areas of application such as engineering and statistics.
