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

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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.