On De la Peña Type Inequalities for Point Processes

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 [5] establishes a nice exponential inequality for discrete time locally square integrable martingale . In this paper, we obtain de la Peña's inequalities for stochastic integral of multivariate point processes. The proof is primarily based on Doléans-Dade exponential formula and the optional stopping theorem.As application, we obtain an exponential inequality for block counting process in Λ−coalescents.