Schmutz, Valentin;
(2022)
Mean-field limit of age and leaky memory dependent Hawkes processes.
Stochastic Processes and their Applications
, 149
pp. 39-59.
10.1016/j.spa.2022.03.006.
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Abstract
We propose a mean-field model of interacting point processes where each process has a memory of the time elapsed since its last event (age) and its recent past (leaky memory), generalizing Age-dependent Hawkes processes. The model is motivated by interacting nonlinear Hawkes processes with Markovian self-interaction and networks of spiking neurons with adaptation and short-term synaptic plasticity. By proving propagation of chaos and using a path integral representation for the law of the limit process, we show that, in the mean-field limit, the empirical measure of the system follows a multidimensional nonlocal transport equation.
| Type: | Article |
|---|---|
| Title: | Mean-field limit of age and leaky memory dependent Hawkes processes |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.spa.2022.03.006 |
| Publisher version: | https://doi.org/10.1016/j.spa.2022.03.006 |
| Language: | English |
| Additional information: | © 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). |
| Keywords: | Hawkes process, Mean-field approximation, Nonlocal transport equation, Propagation of chaos, Erlang kernel, Short-term synaptic plasticity |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences > UCL Queen Square Institute of Neurology UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences > UCL Queen Square Institute of Neurology > Imaging Neuroscience |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10178707 |
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