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

Takahiko Fujita, Shotaro Yagishita and Naohiro Yoshida

Statistics & Probability Letters, 2024, vol. 208, issue C

Abstract: 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.

Keywords: Simple random walk; Martingale; Kennedy martingale; Discrete Azéma–Yor martingale; Discrete Skorokhod embedding (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2024.110076

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