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Keywords = de la Peña’s inequalities

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Article
On De la Peña Type Inequalities for Point Processes
by Naiqi Liu, Vladimir V. Ulyanov and Hanchao Wang
Mathematics 2022, 10(12), 2114; https://doi.org/10.3390/math10122114 - 17 Jun 2022
Cited by 1 | Viewed by 2519
Abstract
There has been a renewed interest in exponential concentration inequalities for stochastic processes in probability and statistics over the last three decades. De la Peña established a nice exponential inequality for a discrete time locally square integrable martingale. In this paper, we obtain [...] Read more.
There has been a renewed interest in exponential concentration inequalities for stochastic processes in probability and statistics over the last three decades. De la Peña established a nice exponential inequality for a discrete time locally square integrable martingale. In this paper, we obtain de la Peña’s inequalities for a stochastic integral of multivariate point processes. The proof is primarily based on Doléans–Dade exponential formula and the optional stopping theorem. As an application, we obtain an exponential inequality for block counting process in Λ−coalescent. Full article
(This article belongs to the Special Issue Limit Theorems of Probability Theory)
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