Extreme Value Theory and Fixed-Domain Asymptotics of Multivariate Random Fields

本计画的目的是发展系统的方法，以建立新颖的结果，并在多元随机场的极值理论与固定区域渐近性上开辟新的研究方向。特别强调的是放置在高斯或非高斯，非平稳和/或各向异性的多元随机场的交叉依赖结构的特点，并研究其对极值理论和固定域渐近的影响。特别是，研究计划结合联合收割机他的调查分形和微分几何的多元随机场的精确估计的漂移概率，参数估计，预测和固定域渐近的多元空间和时空过程。多元随机场模型在统计学、物理学、环境科学和其他科学领域中的需求越来越大，其中许多问题涉及在空间位置获得的具有多元测量的数据集。 随机场模型应用中的常见问题，包括随机场的参数估计、预测和阈值水平的确定。当随机场的观测值在空间和时间上是相关的时，如何准确地确定阈值水平是一个重大的挑战。研究者认为，拟议的研究项目将最终产生新的见解，了解多元空间和时空模型，多元极值理论，并进一步促进其在其他科学领域的适用性。 拟议的活动还将有助于发现青年人才，培训研究生，并发展他们在数学和统计科学方面的职业生涯。

The aim of this project is to develop systematic approach to establish novel results and open new research directions on extreme value theory and fixed-domain asymptotics of multivariate random fields. Special emphasis is placed on characterizing cross-dependence structures of Gaussian or non-Gaussian, non-stationary and/or anisotropic multivariate random fields and on studying their effects on extreme value theory and fixed-domain asymptotics. In particular, the Investigator plans to combine his investigation of fractal and differential geometries of multivariate random fields with precise estimation of the excursion probabilities, parameter estimation, prediction and fixed-domain asymptotics of multivariate spatial and spatio-temporal processes. Multivariate random field models are in increasing demand in statistics, geophysics, environment sciences and other scientific areas, where many problems involve data sets with multivariate measurements obtained at spatial locations. Common problems in applications of random field models including parameter estimation, prediction and the determination of threshold level on the random field. It is a major challenge to accurately determine the threshold level when the observations in the random field are correlated in space and time. The Investigator believes that the proposed research project will ultimately yield novel insights into the understanding of multivariate spatial and spatio-temporal models, multivariate extreme value theory, and further promote their applicability in other scientific areas. The proposed activities will also help to identify young talent, to train graduate students and to develop their careers in the mathematical and statistical sciences.