A limit theorem for the last exit time over a moving nonlinear boundary for a Gaussian process

TL;DR

This paper establishes a limit theorem showing that the scaled last exit time of certain Gaussian stationary processes over a slowly moving nonlinear boundary converges to a Gumbel distribution, revealing asymptotic behavior.

Contribution

It provides the first limit theorem for the distribution of the last exit time over nonlinear boundaries for Gaussian processes, extending previous results on boundary crossing times.

Findings

Last exit time converges to Gumbel distribution

Results apply to a class of Gaussian stationary processes

Enhances understanding of boundary crossing behavior

Abstract

We prove a limit theorem on the convergence of the distributions of the scaled last exit time over a slowly moving nonlinear boundary for a class of Gaussian stationary processes. The limit is a double exponential (Gumbel) distribution.