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Convergence of the temporal averages of a metastable system of spiking neurons

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  • André, Morgan

Abstract

We consider a stochastic system of spiking neurons which was previously proven to present a metastable behavior for a suitable choice of the parameter, in the sense that the time of extinction is asymptotically memory-less when the number of components in the system goes to ∞. In the present article we complete this work by showing that, previous to extinction, the system tends to stabilize in the sense that temporal means taken on an appropriate time scale converge in probability to some fixed value. This property is sometime called thermalization.

Suggested Citation

  • André, Morgan, 2023. "Convergence of the temporal averages of a metastable system of spiking neurons," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 42-68.
    • Handle: RePEc:eee:spapps:v:157:y:2023:i:c:p:42-68
    DOI: 10.1016/j.spa.2022.11.016
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    References listed on IDEAS

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    1. André, Morgan & Planche, Léo, 2021. "The effect of graph connectivity on metastability in a stochastic system of spiking neurons," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 292-310.
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