Extremes of $\alpha(t)$-Locally stationary Gaussian processes with non-constant variances

TL;DR

This paper derives exact tail asymptotics for a class of Gaussian processes with time-varying local stationarity and non-constant variances, revealing new phenomena for specific variance functions.

Contribution

It provides the first precise tail asymptotics for $oldsymbol{ ext{α(t)}}$-locally stationary Gaussian processes with non-constant variances, highlighting new behaviors for certain variance functions.

Findings

Exact tail asymptotics derived for $ ext{α(t)}$-locally stationary Gaussian processes.

Identification of variance functions leading to qualitatively new results.

Extension of previous work by D ext{e}bicki and Kisowski (2007).

Abstract

With motivation from K. D\c{e}bicki and P. Kisowski (2007), in this paper we derive the exact tail asymptotics of $\alpha(t)$-locally stationary Gaussian processes with non-constant variance functions. We show that some certain variance functions lead to qualitatively new results.