Geodesic
Stochastic stability of a system of perfect integrate-and-fire inhibitory neurons
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 971-987

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We study a system of perfect integrate-and-fire inhibitory neurons. It is a system of stochastic processes which interact through receiving an instantaneous increase at the moments they reach certain thresholds. In the absence of interactions, these processes behave as a spectrally positive Lévy processes. Using the fluid approximation approach, we prove convergence to a stable distribution in total variation.
Keywords: spiking neural network, Lévy process, stability, fluid limits. 
@article{SEMR_2020_17_a48,
     author = {T. V. Prasolov},
     title = {Stochastic stability of a system of perfect integrate-and-fire inhibitory neurons},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {971--987},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a48/}
}
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T. V. Prasolov. Stochastic stability of a system of perfect integrate-and-fire inhibitory neurons. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 971-987. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a48/