Probability theory and mathematical statistics

Stochastic stability of a system of perfect integrate-and-fire inhibitory neurons

T. V. Prasolov<sup>ab

a</sup> Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia
^b Mathematical Center in Akademgorodok, 4, Koptyuga ave., Novosibirsk, 630090, Russia

Abstract: 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.

UDC: 519.218.8

MSC: 60B10, 60G51

Received May 11, 2020, published July 20, 2020

Language: English

DOI: 10.33048/semi.2020.17.072

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