Large deviations and applications for Markovian Hawkes processes with a large initial intensity

DOI10.3150/17-BEJ948zbMath1429.60048arXiv1603.07222OpenAlexW2962853874WikidataQ125850244 ScholiaQ125850244MaRDI QIDQ1708987

Xuefeng Gao, Lingjiong Zhu

Publication date: 27 March 2018

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.07222

zbMATH Keywords

large deviationsinsurancequeueing systemsHawkes processeslarge initial intensity

Mathematics Subject Classification ID

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

Related Items (20)

Optimal dividend policy in an insurance company with contagious arrivals of claims ⋮ RUIN PROBABILITIES FOR A MULTIDIMENSIONAL RISK MODEL WITH NON-STATIONARY ARRIVALS AND SUBEXPONENTIAL CLAIMS ⋮ An ephemerally self-exciting point process ⋮ Precise large deviations in a bidimensional risk model with arbitrary dependence between claim-size vectors and waiting times ⋮ Limit theorems for a discrete-time marked Hawkes process ⋮ An expansion formula for Hawkes processes and application to cyber-insurance derivatives ⋮ Asymptotic results for a class of Markovian self-exciting processes ⋮ Diffusion approximation of a risk model with non-stationary Hawkes arrivals of claims ⋮ Unnamed Item ⋮ Large and moderate deviations for a discrete-time marked Hawkes process ⋮ Moderate deviations for a Hawkes-type risk model with arbitrary dependence between claim sizes and waiting times ⋮ Large deviations and applications for Markovian Hawkes processes with a large initial intensity ⋮ Asymptotic analysis for affine point processes with 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 ⋮ Functional limit theorems for nonstationary marked Hawkes processes in the high intensity regime ⋮ Functional central limit theorems for stationary Hawkes processes and application to infinite-server queues ⋮ The microstructure of stochastic volatility models with self-exciting jump dynamics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hawkes processes on large networks
• Gaussian approximation of nonlinear Hawkes processes
• Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes
• Process-level large deviations for nonlinear Hawkes point processes
• Risk processes with non-stationary Hawkes claims arrivals
• Exact simulation of Hawkes process with exponentially decaying intensity
• Limit theorems for Markovian Hawkes processes with a large initial intensity
• Large deviations and applications for Markovian Hawkes processes with a large initial intensity
• Large deviation analysis of the single server queue
• Moderate deviations for Hawkes processes
• Ruin probabilities for risk processes with non-stationary arrivals and subexponential claims
• Large deviations for Markovian nonlinear Hawkes processes
• Limit theorems for nearly unstable Hawkes processes
• Poisson approximation of point processes with stochastic intensity, and application to nonlinear Hawkes processes
• Ruin by dynamic contagion claims
• Some limit theorems for Hawkes processes and application to financial statistics
• Stochastic-Process Limits
• Central Limit Theorem for Nonlinear Hawkes Processes
• Two-parameter Sample Path Large Deviations for Infinite Server Queues
• Limit Theorems for a Cox-Ingersoll-Ross Process with Hawkes Jumps
• Affine Point Processes and Portfolio Credit Risk
• Limit Theorems for Marked Hawkes Processes with Application to a Risk Model
• A new view of the heavy-traffic limit theorem for infinite-server queues
• Long-Time Behavior of a Hawkes Process--Based Limit Order Book
• Affine Point Processes: Approximation and Efficient Simulation
• Large Deviations of Poisson Cluster Processes
• A cluster process representation of a self-exciting process
• Spectra of some self-exciting and mutually exciting point processes

This page was built for publication: Large deviations and applications for Markovian Hawkes processes with a large initial intensity