Browsing by Author "Makasu, Cloud"

Now showing 1 - 3 of 3
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    A note on the stochastic version of the Gronwall lemma
    (Taylor & Francis Group, 2022) Makasu, Cloud
    We prove a stochastic version of the Gronwall lemma assuming that the underlying martingale has a terminal random value in Lp, where 1 p < 1: The proof of the present result is mainly based on a sharp martingale inequality of the Doob-type.
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    On maximal inequalities via comparison principle
    (SpringerOpen, 2015) Makasu, Cloud
    Under certain conditions, we prove a new class of one-sided, weighted, maximal inequalities for a standard Brownian motion. Our method of proof is mainly based on a comparison principle for solutions of a system of nonlinear first-order differential equations.
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    On the exact constants in one-sided maximal inequalitiesfor Bessel processes
    (Taylor and Francis Group, 2023) Makasu, Cloud
    In 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.