Asymptotic behaviors of bivariate Gaussian powered extremes
Wei Zhou, Zuoxiang Peng
TL;DR
This paper investigates the asymptotic behavior of the joint distribution of powered maxima in bivariate Gaussian vectors, deriving limiting distributions and second-order expansions under specific conditions.
Contribution
It introduces new asymptotic results for powered Gaussian maxima, including second-order expansions under the H"usler-Reiss condition.
Findings
Limiting distributions of powered maxima are derived.
Second-order expansions of joint distributions are established.
Results apply under the refined H"usler-Reiss condition.
Abstract
In this paper, joint asymptotics of powered maxima for a triangular array of bivariate powered Gaussian random vectors are considered. Under the H\"usler-Reiss condition, limiting distributions of powered maxima are derived. Furthermore, the second-order expansions of the joint distributions of powered maxima are established under the refined H\"usler-Reiss condition.
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Taxonomy
TopicsFinancial Risk and Volatility Modeling · Insurance, Mortality, Demography, Risk Management · Market Dynamics and Volatility