On Some Problems Concerning the Extremes of a Stationary Process

研究者建议研究与平稳随机过程极值理论有关的三个问题。第一个问题涉及到一个被称为极值指数的量的统计推断，这对相依数据的极值统计理论是重要的。第二个问题涉及对二维随机测量的性质的研究，该测量通过连续时间平稳过程记录高水平的偏移。第三个主题涉及散粒噪声过程的极端情况。对结果的申请将被考虑。这位研究员从事概率领域的工作，也就是极值理论领域。他建议研究三个主题，这三个主题已经被许多其他研究人员在该领域研究过。这些项目中的任何一个的成功完成都将对工程和统计等应用领域产生积极影响。

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.