Mean field limits for nonlinear spatially extended Hawkes processes with exponential memory kernels
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Publication:1756953
DOI10.1016/j.spa.2018.02.007zbMath1404.60069arXiv1703.05031OpenAlexW2953334695WikidataQ98839683 ScholiaQ98839683MaRDI QIDQ1756953
Julien Chevallier, Aline Duarte, Guilherme Ost, Eva Löcherbach
Publication date: 28 December 2018
Published in: Stochastic Processes and their Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1703.05031
Interacting random processes; statistical mechanics type models; percolation theory (60K35) Random measures (60G57) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)
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Cites Work
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- Hawkes processes on large networks
- Mean field limit for disordered diffusions with singular interactions
- Quantitative concentration inequalities for empirical measures on non-compact spaces
- Maximum likelihood identification of neural point process systems
- Dynamics of pattern formation in lateral-inhibition type neural fields
- Mean-field limit of generalized Hawkes processes
- Goodness-of-fit tests and nonparametric adaptive estimation for spike train analysis
- Lasso and probabilistic inequalities for multivariate point processes
- Multi-class oscillating systems of interacting neurons
- Stability of nonlinear Hawkes processes
- Spatiotemporal dynamics of continuum neural fields
- Microscopic approach of a time elapsed neural model
- A cluster process representation of a self-exciting process
- A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue
- Chaoticity for Multiclass Systems and Exchangeability Within Classes
- Spectra of some self-exciting and mutually exciting point processes
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