On the exact constants in one-sided maximal inequalities for Bessel processes

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.

Keywords:

• Bessel processes
• Burkholder-Gundy inequalities
• optimal stopping problem

ACKNOWLEDGEMENT

The author is indebted to the Editor, Associate Editor and an anonymous referee for their useful comments and suggestions which have considerably improved the presentation of this paper.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the author.