Spatial extreme values: variational techniques and stochastic integrals

TL;DR

This paper introduces variational and stochastic integral methods to analyze spatial extreme value processes, providing new formulas and asymptotic results for extremal event statistics in spatial statistics.

Contribution

It develops a novel variational approach and integral formulas for spatial extremal events, extending classical extreme value theory to spatial contexts.

Findings

Derived integral formulas for spatial extremal event statistics

Established asymptotic results analogous to Fisher-Tippett-Gnedenko theory

Discussed applications in spatial statistics and extremal event analysis

Abstract

This work employs variational techniques to revisit and expand the construction and analysis of extreme value processes. These techniques permit a novel study of spatial statistics of the location of minimizing events. We develop integral formulas for computing statistics of spatially-biased extremal events, and show that they are analogous to stochastic integrals in the setting of standard stochastic processes. We also establish an asymptotic result in the spirit of the Fisher-Tippett-Gnedenko theory for a broader class of extremal events and discuss some applications of our results.