CENTRAL LIMIT THEOREMS FOR C(S)-VALUED RANDOM-VARIABLES
CENTRAL LIMIT THEOREMS FOR C(S)-VALUED RANDOM-VARIABLES
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DOI：
10.1016/0022-1236(75)90056-7
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发表时间：
1975-01-01
影响因子：
1.7
通讯作者：
MARCUS, MB
中科院分区：
文献类型：
--
作者：
JAIN, NC;MARCUS, MB
设C (S)是紧度量空间S上的实值连续函数的空间，设{X n， n大于或等于1}是一个独立的同分布C (S)值随机变量序列，其平均值为0，sup tϵs E [X 12 2 (t)]= 1。我们证明了（X 1+···+ X n） n−12在X 1的不同条件下在C (S)上弱收敛于高斯测度，其中一个巩固和推广了Strassen和Dudley、gin<e:1>和Dudley的结果。我们的证明方法不同于这些作者所采用的方法。
Let C (S) be the space of real-valued continuous functions on a compact metric space S. Let {X n, n⩾ 1} be a sequence of independent identically distributed C (S)-valued random variables with mean zero and sup tϵs E [X 1 2 (t)]= 1. We show that the measures induced by (X 1+···+ X n) n− 1 2 converge weakly to a Gaussian measure on C (S) under different conditions on X 1, one of which consolidates and extends results of Strassen and Dudley, Giné, and Dudley. Our method of proof is different from the methods employed by these authors.