On De la Peña Type Inequalities for Point Processes

Naiqi Liu, Vladimir V. Ulyanov and Hanchao Wang
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Naiqi Liu: School of Mathematics, Shandong University, Jinan 250100, China
Vladimir V. Ulyanov: Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow, Russia
Hanchao Wang: Institute for Financial Studies, Shandong University, Jinan 250100, China

Mathematics, 2022, vol. 10, issue 12, 1-13

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 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.

Keywords: de la Peña’s inequalities; purely discontinuous local martingales; stochastic integral of multivariate point processes; Doléans–Dade exponential (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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