On the exact constants in one-sided maximal inequalities for Bessel processes. Issue 1 (2nd January 2023)

• Record Type: Journal Article
• Authors: Makasu, Cloud
• Is Part Of: Sequential analysis. Volume 42:Issue 1(2023)
• Page Start: 35
• Page End: 42
• Publication Date: 2023-01-02
• Subjects: Bessel processes -- Burkholder-Gundy inequalities -- optimal stopping problem; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2022.2150778
• Languages: English
• ISSNs: 0747-4946

Abstract

Abstract: In this paper, we establish a one-sided maximal moment inequality with exact constants for Bessel processes. As a consequence, we obtain an exact constant in the Burkholder-Gundy inequality. The proof of our main result is based on a pure optimal stopping problem of the running maximum process for a Bessel process. The present results extend and complement a number of related results previously known in the literature.