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arXiv · 2204.08602

On De la Pe\~{n}a Type Inequalities for Point Processes

Naiqi Liu·Vladimir V. Ulyanov·Hanchao Wang
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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 Pe\~{n}a \cite{d} establishes a nice exponential inequality for discrete time locally square integrable martingale . In this paper, we obtain de la Pe\~{n}a's inequalities for stochastic integral of multivariate point processes. The proof is primarily based on Dol\'{e}ans-Dade exponential formula and the optional stopping theorem. As application, we obtain an exponential inequality for block counting process in $\Lambda-$coalescents.

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Naiqi Liu, Vladimir V. Ulyanov, Hanchao Wang. 2022-04-19. On De la Pe\~{n}a Type Inequalities for Point Processes. https://arxiv.org/abs/2204.08602

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