THE ENTROPY OF A RANDOMLY STOPPED SEQUENCE

被引：10

作者：

EKROOT, L ^{[1
]}

COVER, TM ^{[1
]}

机构：

[1] STANFORD UNIV,DEPT STAT,STANFORD,CA 94305

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 1991年 / 37卷 / 06期

基金：

美国国家科学基金会;

关键词：

ENTROPY; STOPPING TIME; WALD EQUATION; STOPPED SEQUENCES;

D O I：

10.1109/18.104324

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

A Wald-like equation is proved for the entropy of a randomly stopped sequence of independent identically distributed discrete random variables X1, X2, ... with a nonanticipating stopping time N. Specifically, it is shown that H(X(N)) = (EN)H(X1) + H(N\X infinity), where X(N) denotes the randomly stopped sequence. Thus, the randomness in the stopped sequence X(N) is the expected number of "calls" for X times the entropy per call plus the residual randomness in the stopping time conditioned on the unstopped sequence X infinity.

引用

页码：1641 / 1644

页数：4