Asymptotic Behaviors Of Powered-extremes Of Bivariate Gaussian Triangular Array

This thesis mainly investigates asymptotic behaviors of powered extremes of bivariate Gaussian triangular arrays.Let Xn ndenote the maximum of Gaussian sequence and |Xn,n|p he the powered-extremes with power index p>0.The results show that,under the case of bivariate Gaussian triangular arrays,the convergence rates and higher-order expansions of powered-extremes has no relation to the power index p.The thesis is organized as the following two parts.For the first part,we show that,under the Husler-Reiss condition?joint limit distributions of powered maxima is the Husler-Reiss max-stable distribution.In the second part,under the refined Husler-Reisscondition,the second-order expan-sions of the joint distributions of powered maxima are established.The main results show that,under the case of bivariate Gaussian triangular arrays,the convergence rates of the joint limit distribution still has the same order as 1/log n.