Some martingale properties of the simple random walk and its maximum process

被引：0
|
作者：
Fujita, Takahiko [1 ]
Yagishita, Shotaro [2 ]
Yoshida, Naohiro [3 ]
机构：
[1] Chuo Univ, Dept Data Sci Business Innovat, 1-13-27 Kasuga,Bunkyo Ku, Tokyo 1128551, Japan
[2] Chuo Univ, Dept Ind & Syst Engn, 1-13-27 Kasuga,Bunkyo Ku, Tokyo 1128551, Japan
[3] Keiai Univ, Dept Econ, 1-5-21 Anagawa,Inage ku, Chiba, Chiba 2638588, Japan
来源：
STATISTICS & PROBABILITY LETTERS | 2024年 / 208卷
关键词：
Simple random walk; Martingale; Kennedy martingale; Discrete Azema-Yor martingale; Discrete Skorokhod embedding;
D O I：
10.1016/j.spl.2024.110076
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：
Martingales related to simple random walks and their maximum processes are investigated, and characterizations of those martingales are obtained. As applications, derivation of the Kennedy martingale, proofs of the corresponding Doob inequalities, and a solution to the Skorokhod embedding problem are presented.
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页数：8
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