Sharp large deviation estimates for Gaussian extrema

2025/12/20 by José M. Zapata, Zapata, José M.
Decision Sciences · Economics, Econometrics and Finance · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.2512.18297

openalex publication_date 2025/12/20 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28

Abstract

We establish sharp large-deviation asymptotic estimates for the maximum order statistic of i.i.d. standard normal random variables on all Borel subsets of the positive real line. This result yields more accurate tail approximations than the classical Gumbel limit.

Citations

• Large Deviations of Bivariate Gaussian Extrema
• Limiting forms of the frequency distribution of the largest or smallest member of a sample

Related

• Sharp large deviation results for sums of independent random variables
• Revisit on the convergence rate of normal extremes
• Large deviations in Selberg's central limit theorem
• Large deviations for the maximum and reversed order statistics of Weibull-like variables
• Dominating Points of Gaussian Extremes