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