Limit Theorems for Marked Hawkes Processes with Application to a Risk Model

DOI10.1080/15326349.2015.1024868zbMath1325.60025arXiv1211.4039OpenAlexW2594472342MaRDI QIDQ3194561

Lingjiong Zhu, Dmytro Karabash

Publication date: 20 October 2015

Published in: Stochastic Models (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.4039

zbMATH Keywords

central limit theoremlarge deviation principlemarked point processesrisk modelHawkes processesself-exciting processes

Mathematics Subject Classification ID

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Cites Work

• Process-level large deviations for nonlinear Hawkes point processes
• Risk processes with non-stationary Hawkes claims arrivals
• Moderate deviations for Hawkes processes
• Ruin probabilities for risk processes with non-stationary arrivals and subexponential claims
• Large deviations for Markovian nonlinear Hawkes processes
• Some limit theorems for Hawkes processes and application to financial statistics
• Central Limit Theorem for Nonlinear Hawkes Processes
• Limit Theorems for a Cox-Ingersoll-Ross Process with Hawkes Jumps
• Rate of convergence to equilibrium of marked Hawkes processes
• Large Deviations of Poisson Cluster Processes
• Distributions that are both subexponential and in the domain of attraction of an extreme-value distribution
• A cluster process representation of a self-exciting process
• Large deviations

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