Demmartingales and the functionnal Hill process for small parameters

TL;DR

This paper uses demimartingale techniques to analyze the asymptotic behavior of the functional Hill process for small parameters in Extreme Value Theory, providing new insights into dependent random variables.

Contribution

It introduces a novel application of demimartingale methods to derive the asymptotic law of the functional Hill process for small parameters.

Findings

Established the asymptotic law of the demimartingale

Derived the asymptotic behavior of the functional Hill process for small parameters

Demonstrated the effectiveness of demimartingale techniques in EVT

Abstract

Association of random variables and Demimartingales are recent fields for handling asymptotic behaviors of sums of dependent random variables. We apply their techniques to establish the asymptotic law of a demimartingale We next apply the results to find the asymptotic behavior the functional Hill process for small parameters within the Extreme Value Theory (EVT) field. Such a result would have been very hard to find whithout demimartingales techniques.