一致混合序列最大值的强极限律  

STRONG LIMIT LAWS OF MAXIMA OF UNIFORMLY MIXING SEQUENCES

作　　者：潘家柱[1] 

机构地区：[1]东北师范大学数学系,长春130024

出　　处：《系统科学与数学》1992年第2期189-192,共4页Journal of Systems Science and Mathematical Sciences

摘　　要：设{X_i}是一个随机变量序列,用(?)(X_i,1≤j≤m)和(?)(X_j,j≥m)分别表示由(X_1,…,X_m)和(X_m,X_(m+1),…)产生的 σ-域.若对任意 A∈(?)(X_j,1≤j≤m)和 B∈(?)(X_j,j≥m+l+1)有|P(A∩B)—P(A)·P(B)|<g(l),(1)其中 g(l)→0(l→+∞),则称{X_i}为一致混合序列(uniformly mixing sequence).本文先将著名的 Kolmogorov 0—1律推广到一致混合序列。In this paper,Kolmogorov 0—1 law is extended to uniformly mixing sequences,and by usingthis result,the strong limit laws of maxima of uniformly mixing sequences are discussed.Inaddition,a satisfactory result on maxima of i.i.d sequences is obtained.

关 键 词：一致混合序列 最大值 强极限律 

分 类 号：O211.5[理学—概率论与数理统计]