Mean-field limit of age and leaky memory dependent Hawkes processes

Valentin Schmutz

Stochastic Processes and their Applications, 2022, vol. 149, issue C, 39-59

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.

Keywords: Hawkes process; Mean-field approximation; Nonlocal transport equation; Propagation of chaos; Erlang kernel; Short-term synaptic plasticity (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:149:y:2022:i:c:p:39-59

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DOI: 10.1016/j.spa.2022.03.006

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