Poisson approximation of point processes with stochastic intensity, and application to nonlinear Hawkes processes

DOI10.1214/15-AIHP730zbMath1367.60020MaRDI QIDQ2357265

Giovanni Luca Torrisi

Publication date: 13 June 2017

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.aihp/1491897741

zbMATH Keywords

Malliavin calculusClark-Ocone formulapoint processesconfidence intervalPoisson approximationHawkes processstochastic intensityChen-Stein methodErlang loss system

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Queueing theory (aspects of probability theory) (60K25) Stochastic integrals (60H05) Stochastic calculus of variations and the Malliavin calculus (60H07) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (7)

Some asymptotic results for nonlinear Hawkes processes ⋮ Malliavin calculus for marked binomial processes and applications ⋮ Bayesian estimation of nonlinear Hawkes processes ⋮ Large deviations and applications for Markovian Hawkes processes with a large initial intensity ⋮ Precise deviations for Hawkes processes ⋮ Unnamed Item ⋮ Functional central limit theorems and moderate deviations for Poisson cluster processes

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