# Asymptotic normality of high level-large time crossings of a Gaussian process

## TL;DR

This paper proves that the standardized count of high-level crossings in a stationary Gaussian process becomes normally distributed as both the crossing level and observation time grow large, under certain conditions.

## Contribution

It establishes the asymptotic normality of high-level crossings for Gaussian processes when both level and time tend to infinity, extending previous results to a broader setting.

## Key findings

- Standardized crossings follow a normal distribution asymptotically.
- Results apply to stationary mixing Gaussian processes.
- The expected number of crossings diverges as level and time increase.

## Abstract

We prove the asymptotic normality of the standardized number of crossings of a centered stationary mixing Gaussian process when both the level and the time horizon go to infinity in such a way that the expected number of crossings also goes to infinity.