Functional limit theorems for marked Hawkes point measures

DOI10.1016/j.spa.2020.12.002zbMath1469.60160arXiv1908.06703OpenAlexW3117567326MaRDI QIDQ2021389

Ulrich Horst, Wei Xu

Publication date: 27 April 2021

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

Full work available at URL: https://arxiv.org/abs/1908.06703

zbMATH Keywords

functional limit theoremHawkes point measuremarked Hawkes process

Mathematics Subject Classification ID

Random measures (60G57) Functional limit theorems; invariance principles (60F17) Microbiology (92C70)

Related Items

The Malliavin-Stein method for Hawkes functionals, Limit theorems for a discrete-time marked Hawkes process, Multivariate Hawkes processes with simultaneous occurrence of excitation events coming from different sources, Large and moderate deviations for a discrete-time marked Hawkes process, 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

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• Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes
• A plea for stochastic population dynamics
• Risk processes with non-stationary Hawkes claims arrivals
• A limit theorem on a subcritical Galton-Watson process with immigration
• Limit theorems for the integrals of some branching processes
• Limit theorems for the integral of a population process with immigration
• A central limit theorem for martingales and an application to branching processes
• Limit theorems for Markovian Hawkes processes with a large initial intensity
• Large deviations and applications for Markovian Hawkes processes with a large initial intensity
• The microstructural foundations of leverage effect and rough volatility
• Limit theorems for non-Markovian marked dynamic contagion processes
• Small and large time scale analysis of a network traffic model
• Explosive Poisson shot noise processes with applications to risk reserves
• Ruin probabilities for risk processes with non-stationary arrivals and subexponential claims
• Limit theorems for nearly unstable Hawkes processes
• Some limit theorems for Hawkes processes and application to financial statistics
• Rate of convergence to equilibrium of marked Hawkes processes
• A dynamic contagion process
• Limit Theorems for Marked Hawkes Processes with Application to a Risk Model
• Large Deviations of Poisson Cluster Processes
• Power spectra of general shot noises and Hawkes point processes with a random excitation
• Delay in claim settlement and ruin probability approximations
• A Scaling Limit for Limit Order Books Driven by Hawkes Processes
• Branching Processes
• Spectra of some self-exciting and mutually exciting point processes