具有随机足标的弱相依高斯序列最大值的极限分布

On the Limiting Distribution of the Maximum of Weakly Dependent Gaussian Sequence with Random Index

设ξ_1,ξ_2,…为标准化的平稳高斯序列,M_n=max(1≦i≦n)ξ_i,协方差r_n=Cov(ξ_1,ξ_(n+1))= E(ξ_1ξ_(n+1)).{N(n)}为一列取正整数的随机变量,满足(N(n))/n■η>0,n→∞.在条件r_n logn→0,n→∞之下,给出了M_(N(n))的极限分布.

Letξ1,ξ2,… be a standard stationary Gaussian sequence, and Mn=max（1≦i≦n）ξi, rn=Cov（ξ1,ξ（n＋1））= E（ξ1ξ（n＋1））.Suppose {N（n）} is a non-negative integer valued random variable with （N（n））/n p→η〉0,n→∞. When rn logn→0,n→∞ the limiting distribution of MN（n） is derived.