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Stochastic stability of a system of perfect integrate-and-fire inhibitory neurons. / Prasolov, Timofei Vycheslavovich.

In: Siberian Electronic Mathematical Reports, Vol. 17, 2020, p. 971-987.

Research output: Contribution to journal › Article › peer-review

Harvard

Prasolov, TV 2020, 'Stochastic stability of a system of perfect integrate-and-fire inhibitory neurons', Siberian Electronic Mathematical Reports, vol. 17, pp. 971-987. https://doi.org/10.33048/semi.2020.17.072

APA

Prasolov, T. V. (2020). Stochastic stability of a system of perfect integrate-and-fire inhibitory neurons. Siberian Electronic Mathematical Reports, 17, 971-987. https://doi.org/10.33048/semi.2020.17.072

Vancouver

Prasolov TV. Stochastic stability of a system of perfect integrate-and-fire inhibitory neurons. Siberian Electronic Mathematical Reports. 2020;17:971-987. doi: 10.33048/semi.2020.17.072

Author

Prasolov, Timofei Vycheslavovich. / Stochastic stability of a system of perfect integrate-and-fire inhibitory neurons. In: Siberian Electronic Mathematical Reports. 2020 ; Vol. 17. pp. 971-987.

BibTeX

@article{156af466b3e6438b94644b6e986a239b,
title = "Stochastic stability of a system of perfect integrate-and-fire inhibitory neurons",
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 L{\'e}vy processes. Using the fluid approximation approach, we prove convergence to a stable distribution in total variation.",
keywords = "fluid limits, L{\'e}vy process, spiking neural network, stability",
author = "Prasolov, {Timofei Vycheslavovich}",
note = "Funding Information: Prasolov, T.V., Stochastic stability of a system of perfect integrate-and-fire inhibitory neurons. {\textcopyright} 2020 Prasolov T.V. Research was financially supported by RSF grant No. 17 − 11 − 01173. Received May, 11, 2020, published July, 20, 2020.",
year = "2020",
doi = "10.33048/semi.2020.17.072",
language = "English",
volume = "17",
pages = "971--987",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",

}

RIS

TY - JOUR

T1 - Stochastic stability of a system of perfect integrate-and-fire inhibitory neurons

AU - Prasolov, Timofei Vycheslavovich

N1 - Funding Information: Prasolov, T.V., Stochastic stability of a system of perfect integrate-and-fire inhibitory neurons. © 2020 Prasolov T.V. Research was financially supported by RSF grant No. 17 − 11 − 01173. Received May, 11, 2020, published July, 20, 2020.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - fluid limits

KW - Lévy process

KW - spiking neural network

KW - stability

UR - http://www.scopus.com/inward/record.url?scp=85099207413&partnerID=8YFLogxK

U2 - 10.33048/semi.2020.17.072

DO - 10.33048/semi.2020.17.072

M3 - Article

AN - SCOPUS:85099207413

VL - 17

SP - 971

EP - 987

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -

ID: 27504328