FAIR COIN-TOSSING GAMES

被引：10

作者：

CHEN, R

ZAME, A

机构：

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 1979年 / 9卷 / 01期

关键词：

fair coin-tossing game; fair coin-tossing process; stopping time; the Conway Algorithm; the renewal theorem; the taboo first passage probability;

D O I：

10.1016/0047-259X(79)90073-3

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let Ω be a finite set with k elements and for each integer n ≧ 1 let Ωn = Ω × Ω × ... × Ω (n-tuple) and Ωn = {(a1, a2,..., an) | (a1, a2,..., an) ∈ Ωn and aj ≠ aj+1 for some 1 ≦ j ≦ n - 1}. Let {Ym} be a sequence of independent and identically distributed random variables such that P(Y1 = a) = k-1 for all a in Ω. In this paper, we obtain some very surprising and interesting results about the first occurrence of elements in Ωn and in Ω̄n with respect to the stochastic process {Ym}. The results here provide us with a better and deeper understanding of the fair coin-tossing (k-sided) process. © 1979.

引用

页码：150 / 156

页数：7