Renewal in Hawkes processes with self-excitation and inhibition

DOI10.1017/apr.2020.19zbMath1473.60081arXiv1801.04645OpenAlexW2782577402MaRDI QIDQ5005038

Manon Costa, Carl Graham, Viet Chi Tran, Laurence Marsalle

Publication date: 4 August 2021

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.04645

zbMATH Keywords

point processesinhibitionconcentration inequalitiesGalton-Watson treesself-excitation\(m/G/\infty\) queuesergodic limit theorems

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Laplace transform (44A10) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Limit theorems in probability theory (60F99) Renewal theory (60K05)

Related Items (17)

Interacting Hawkes processes with multiplicative inhibition ⋮ Limit theorems for Hawkes processes including inhibition ⋮ Multivariate Hawkes processes on inhomogeneous random graphs ⋮ The Malliavin-Stein method for Hawkes functionals ⋮ Stability for Hawkes processes with inhibition ⋮ An expansion formula for Hawkes processes and application to cyber-insurance derivatives ⋮ Multivariate Hawkes processes with simultaneous occurrence of excitation events coming from different sources ⋮ Bayesian estimation of nonlinear Hawkes processes ⋮ On extremes of random clusters and marked renewal cluster processes ⋮ Asymptotic deviation bounds for cumulative processes ⋮ Inference of multivariate exponential Hawkes processes with inhibition and application to neuronal activity ⋮ On a Finite-Size Neuronal Population Equation ⋮ A palm space approach to non-linear Hawkes processes ⋮ Normal approximation of compound Hawkes functionals ⋮ Mean field limits for interacting Hawkes processes in a diffusive regime ⋮ Regenerative properties of the linear Hawkes process with unbounded memory ⋮ Mean-field limits for non-linear Hawkes processes with excitation and inhibition

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