Exact Asymptotic for the Tail of Maximum of Smooth Random Field Distribution

TL;DR

This paper derives an exact asymptotic expression for the tail probability of the maximum of a smooth random field using the saddle point method, providing precise probabilistic estimates.

Contribution

It introduces a novel application of the saddle point method to obtain exact asymptotics for the maximum of smooth random fields.

Findings

Derived explicit asymptotic formulas for tail probabilities.

Enhanced understanding of the distribution of maxima in smooth random fields.

Potential applications in fields requiring precise extreme value analysis.

Abstract

We obtain in this paper using the saddle point method the expression for the exact asymptotic for the tail of maximum of smooth (twice continuous differentiable) random field (process) distribution.