Mathematical Sciences: Statistics and Probability Theory of Extremes and Stable Processes

这项研究涉及各种相互关联的 有关极值、因变量和 稳定的过程。许多数学问题 重要的实际应用。 研究重点是 估计的分布的极端和使用作为其 一个点过程的弱收敛， 记录了极端的情况 统计推断的研究 极值包括调查的性质， 极值指标和边际尾分布的估计 弱相依变量;渐近理论的研究 因变量的总和试图定义大类的 可以建立趋同的过程;以及问题 在稳定过程的推断中考虑了协调稳定 过程和移动平均稳定过程。

This research addresses a wide variety of interrelated problems concerning extremes, sums of dependent variables and stable processes. Many of these mathematical problems have important practical applications. The research focusses on the estimation of the distributions of extremes and uses as its principal tool the weak convergence of a point process which records the extremes. The research in statistical inference for extreme values includes investigation of properties of the extremal index and estimation of marginal tail distributions for weakly dependent variables; the research on asymptotic theory for sums of dependent variables seeks to define large classes of processes for which convergence can be established; and problems in inference for stable processes considers harmonizable stable processes and the moving average stable process.