多维随机变量序列的最大值和最小值的渐近独立性

THE ASYMPTOTIC INDEPENDENCE OF THE MAXIMA AND THE MINIMU OF MULTIVARIATE RANDOM VARIABLE SEQUENCES

摘要: 设X_n=(X_1n,X_2n,…,X_mn,n≥1是i.i.d.的m维随机向量序列,Z_in=maxX_i1,X_i2,…,X_in,W_in=minX_i1,X_i2,…,X_in,1≤i≤m,Z_n=(Z_1n,Z_2n,…,Z_mn),W_n=(W_1n,W_2n…,W_mn).本文得出了W_n与Z_n渐近独立的充分必要条件.

Abstract: LetX_n=(X_1n,X_2n,…,X_mn,n≥1 be i.i.d. m-dimensional random Vector Sequence, Z_in=maxX_i1,X_i2,…,X_in,W_in=minX_i1,X_i2,…,X_in,1≤i≤m,Z_n=(Z_1n,Z_2n,…,Z_mn),W_n=(W_1n,W_2n…,W_mn).The necessary and sufficient conditions are found for the asymptotic independence of Z_n and W_n.