LIMIT LAWS FOR ERGODIC PROCESSES
LIMIT LAWS FOR ERGODIC PROCESSES
复制标题
遍历过程的极限定律
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
B. Weiss
中科院分区：
文献类型：
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作者：
J. Thouvenot;B. Weiss
随机变量序列的归一化和的极限律研究是概率论中的经典课题之一。本文给出了两个结果，证明遍历平稳过程可以允许任意分布作为归一化和的极限。在第一种情况下，我们取前n个变量的平均值，但是这个过程是不可积的。在第二种情况下，变量只取两个值，并归纳地构造正则化常数序列。在这两种情况下，过程都可以定义为任意非周期测度保持系统的因子。
The study of limit laws for normalized sums of a sequence of random variables is one of the classical topics in probability theory. We give here two results showing that ergodic stationary processes can admit an arbitrary distribution as the limit of normalized sums. In the first, we take the usual average of the first n variables, but the process is not integrable. In the second, the variables take on only two values and the sequence of normalizing constants is constructed inductively. In both cases the processes can be defined as factors of an arbitrary aperiodic measure preserving system.