(xk,k≥1)为d维高斯序列,M(n)与re(n)表(xk,1≤k≤n)的最大值与最小值.本文在其相关系数列(rij,(k,l):1≤i,J≤d;k,l≥1)满足一定条件下,得到此序列最大值与最小值联合极限分布及几乎处处收敛定理.
Let {Xk, k 〉 1} be a d-variate Gaussian vector sequence with Xk = (Xkl,..., Xkd). Denote its partial maxima and minima respectively by M(n) = (Mnl,..', Mnd) and re(n) = (rnnl,-.., mnd), where Mni = max{Xki, 1 〈 k 〈 n}, toni : min{Xki, 1 〈 k 〈 n}. The joint limiting distribution and joint version of the almost sure convergence for the maxima and minima are derived under some conditions, respectively.