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

本研究解决了有关极值、因变量和稳定过程的各种相互关联的问题。这些数学问题中有许多具有重要的实际应用。研究的重点是极值分布的估计，并将记录极值的点过程的弱收敛性作为估计极值分布的主要工具。极值的统计推断研究包括极值指数的性质研究和弱因变量边际尾分布的估计；因变量和的渐近理论研究试图定义可以建立收敛性的大类过程；稳定过程的推理问题考虑了可调和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.