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A note on the stochastic version of the Gronwall lemma
(Taylor & Francis Group, 2022)
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 ...
On maximal inequalities via comparison principle
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 ...
On the exact constants in one-sided maximal inequalitiesfor Bessel processes
(Taylor and Francis Group, 2023)
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 ...