The asymptotic distribution of maxima of stationary random sequences under random replacing

TL;DR

This paper studies how random replacements affect the extreme values of stationary sequences with dependencies, deriving their joint asymptotic distribution and demonstrating applications of these results.

Contribution

It introduces a novel analysis of the joint asymptotic distribution of maxima in stationary sequences with random replacements under dependency conditions.

Findings

Derived the joint asymptotic distribution of maxima

Analyzed effects of random replacing on extremes

Provided applications for the theoretical results

Abstract

In this paper, we investigated the effect on extreme of random replacing for a stationary sequence satisfying a type of long dependent condition and a local dependent condition, and derived the joint asymptotic distribution of maximum from the stationary sequence and the maximum from the random replacing sequence. We also provided several applications for our main results.