Process-level large deviations for nonlinear Hawkes point processes

DOI10.1214/12-AIHP532zbMath1296.60129arXiv1108.2431MaRDI QIDQ405494

Lingjiong Zhu

Publication date: 5 September 2014

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

Full work available at URL: https://arxiv.org/abs/1108.2431

zbMATH Keywords

rare eventslarge deviationspoint processesHawkes processesself-exciting processes

Mathematics Subject Classification ID

Large deviations (60F10) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (22)

Some asymptotic results for nonlinear Hawkes processes ⋮ Limit theorems for Hawkes processes including inhibition ⋮ Affine Point Processes: Approximation and Efficient Simulation ⋮ Limit Theorems for a Cox-Ingersoll-Ross Process with Hawkes Jumps ⋮ Limit Theorems for Marked Hawkes Processes with Application to a Risk Model ⋮ Limit theorems for the compensator of Hawkes processes ⋮ Limit theorems for a discrete-time marked Hawkes process ⋮ Mean-field limit of generalized Hawkes processes ⋮ Unnamed Item ⋮ Moderate deviations for marked Hawkes processes ⋮ Asymptotic results for a class of Markovian self-exciting processes ⋮ Unnamed Item ⋮ Large and moderate deviations for a discrete-time marked Hawkes process ⋮ Limit theorems for an extended inverse Hawkes process with general exciting functions ⋮ Large deviations and applications for Markovian Hawkes processes with a large initial intensity ⋮ Precise deviations for Hawkes processes ⋮ Limit theorems for inverse process \(T_n\) of Hawkes process ⋮ Asymptotics for Hawkes processes with large and small baseline intensities ⋮ Limit theorems for an inverse Markovian Hawkes process ⋮ An extension of Hawkes processes with ephemeral nearest effects ⋮ Large deviations for Markovian nonlinear Hawkes processes ⋮ Limit theorems for discrete Hawkes processes

Cites Work

• Unnamed Item
• Unnamed Item
• Risk processes with non-stationary Hawkes claims arrivals
• An introduction to the theory of point processes
• Some limit theorems for Hawkes processes and application to financial statistics
• Stability of nonlinear Hawkes processes
• Central Limit Theorem for Nonlinear Hawkes Processes
• Large Deviations of Poisson Cluster Processes
• Asymptotic evaluation of certain markov process expectations for large time. IV
• Point processes and random measures
• Spectra of some self-exciting and mutually exciting point processes
• Large deviations

This page was built for publication: Process-level large deviations for nonlinear Hawkes point processes