On De la Peña Type Inequalities for Point Processes

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 l...

Full description

Bibliographic Details
Main Authors: Naiqi Liu, Vladimir V. Ulyanov, Hanchao Wang
Format: Article
Language:English
Published: MDPI AG 2022-06-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/10/12/2114
Description
Summary: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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Λ</mo><mo>−</mo></mrow></semantics></math></inline-formula>coalescent.
ISSN:2227-7390