Limit theorems for Markovian Hawkes processes with a large initial intensity

DOI10.1016/j.spa.2017.12.001zbMath1409.60078arXiv1512.02155OpenAlexW2963588348MaRDI QIDQ1615912

Lingjiong Zhu, Xuefeng Gao

Publication date: 31 October 2018

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.02155

zbMATH Keywords

asymptotic regimeHawkes processesclustering effect

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Large deviations (60F10) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (13)

Numerical method for means of linear Hawkes processes ⋮ Limit theorems for a discrete-time marked Hawkes process ⋮ Matrix calculations for moments of Markov processes ⋮ Asymptotic results for a class of Markovian self-exciting processes ⋮ Unnamed Item ⋮ Large deviations and applications for Markovian Hawkes processes with a large initial intensity ⋮ Precise deviations for Hawkes processes ⋮ Limit theorems for non-Markovian marked dynamic contagion processes ⋮ Functional limit theorems for marked Hawkes point measures ⋮ Limit theorems for an inverse Markovian Hawkes process ⋮ Unnamed Item ⋮ Functional limit theorems for nonstationary marked Hawkes processes in the high intensity regime ⋮ The microstructure of stochastic volatility models with self-exciting jump dynamics

Cites Work

• Unnamed Item
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• Maximum likelihood estimation of Hawkes' self-exciting point processes
• Hawkes processes on large networks
• Statistical inference versus mean field limit for Hawkes processes
• Modelling security market events in continuous time: intensity based, multivariate point process models
• Gaussian approximation of nonlinear Hawkes processes
• Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes
• Weak limit theorems for stochastic integrals and stochastic differential equations
• Stopping times and tightness. II
• A survey and some generalizations of Bessel processes
• Mean-field limit of generalized Hawkes processes
• Modelling irregulary spaced financial data. Theory and practice of dynamic duration models.
• Moderate deviations for Hawkes processes
• Large deviations for Markovian nonlinear Hawkes processes
• Limit theorems for nearly unstable Hawkes processes
• Exponential moments of affine processes
• Some limit theorems for Hawkes processes and application to financial statistics
• Stability of nonlinear Hawkes processes
• Central Limit Theorem for Nonlinear Hawkes Processes
• Equivalence of Stochastic Equations and Martingale Problems
• Affine Point Processes and Portfolio Credit Risk
• Large Deviations of Poisson Cluster Processes
• A cluster process representation of a self-exciting process
• An Introduction to the Theory of Point Processes
• Hawkes processes with variable length memory and an infinite number of components
• Spectra of some self-exciting and mutually exciting point processes

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