A NOTE ON THE MAXIMUM OF A RANDOM-WALK

被引：1
|
作者：
STADJE, W [1 ]
机构：
[1] UNIV OSNABRUCK,FACHBEREICH MATH INFORMAT,D-49069 OSNABRUCK,GERMANY
来源：
STATISTICS & PROBABILITY LETTERS | 1995年 / 23卷 / 03期
关键词：
INTEGER-VALUED RANDOM WALK; MAXIMUM; MOMENT-GENERATING FUNCTION;
D O I：
10.1016/0167-7152(94)00117-Q
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：
For an integer-valued, aperiodic random walk (S-n)(n greater than or equal to 1) with negative drift we consider its maximum M and M(+), its maximum before first attaining a nonpositive value. As a converse to well-known results on the asymptotic behavior of m(n) = P(M greater than or equal to n) and r(n) = P(M(+) greater than or equal to n), it is shown that any of the relations m(n) similar to cr(-n) or r(n) similar to cr(-n) (c > 1, r > 1) implies that E(r(S1)) = 1.
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页码：227 / 231
页数：5
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