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

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  • Schmutz, Valentin

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.

Suggested Citation

  • Schmutz, Valentin, 2022. "Mean-field limit of age and leaky memory dependent Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 39-59.
    • Handle: RePEc:eee:spapps:v:149:y:2022:i:c:p:39-59
    DOI: 10.1016/j.spa.2022.03.006
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    1. Jonathan W. Pillow & Jonathon Shlens & Liam Paninski & Alexander Sher & Alan M. Litke & E. J. Chichilnisky & Eero P. Simoncelli, 2008. "Spatio-temporal correlations and visual signalling in a complete neuronal population," Nature, Nature, vol. 454(7207), pages 995-999, August.
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    6. Alan G. Hawkes, 2018. "Hawkes processes and their applications to finance: a review," Quantitative Finance, Taylor & Francis Journals, vol. 18(2), pages 193-198, February.
    7. Richard Naud & Wulfram Gerstner, 2012. "Coding and Decoding with Adapting Neurons: A Population Approach to the Peri-Stimulus Time Histogram," PLOS Computational Biology, Public Library of Science, vol. 8(10), pages 1-14, October.
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