Research Articles (Mathematics)
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Item On the exact constants in one-sided maximal inequalitiesfor Bessel processes(Taylor and Francis Group, 2023) Makasu, CloudIn this paper, we establish a one-sided maximal moment inequalitywith exact constants for Bessel processes. As a consequence, weobtain an exact constant in the Burkholder-Gundy inequality. Theproof of our main result is based on a pure optimal stopping prob-lem of the running maximum process for a Bessel process. The pre-sent results extend and complement a number of related resultspreviously known in the literature.Item One-sided maximal inequalities for a randomly stopped bessel process(Taylor & Francis Group, LLC, 2023) Cloud, MakasuWe prove a one-sided maximal inequality for a randomly stopped Bessel process of dimension (Formula presented.) 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.