一类马尔可夫序列最大值的极限律

Limit Laws for the Maximum of a Class Markov Sequences

主要研究一类马尔可夫序列{Xn,n≥0}的最大值的极限分布.导出了这类序列最大值和最小值的分布表达式,利用经典极值理论,建立了规范化最大值max{X0,X1,…,Xn}与i.i.d序列{ξn,n≥1}的规范化最大值max{1ξ,2ξ,…,ξn+1}具有相同极限律的条件.

We mainly study the limiting distribution of maximum of a class Markov sequence {Xn, ,n≥0}. We derive the expressions of distribution of the maximum and minmum, and establish conditions under which the limit law of max （X0 ,X1 ,…,Xn） coincides with that the max（ξ1 ,ξ2,…,ξn-1 ） when both are appropriately normed, where {ξn,n≥1} is a i. i. d random sequence.