Abstract
We prove a one-sided maximal inequality for a randomly stopped Bessel process of dimension For the special case when α = 1, we obtain a sharp Burkholder-Gundy inequality for Brownian motion as a consequence. An application of the present results is also given.
ACKNOWLEDGEMENTS
The valuable suggestions and comments by the handling editors, and anonymous referees are gratefully acknowledged. It is also a pleasure to thank Professor M. Abundo at the Universita di Roma Tor Vergata (Italy) for drawing the author’s attention to reference (Abundo Citation2017) which motivated this work. Part of this work was written while on leave of absence and visiting the Department of Maths, University of Zimbabwe.
DISCLOSURE
The author has no conflicts of interest to report.