Počet záznamů: 1
Shot noise, weak convergence and diffusion approximations
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SYSNO ASEP 0541564 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Shot noise, weak convergence and diffusion approximations Tvůrce(i) Tamborrino, M. (GB)
Lánský, Petr (FGU-C) RID, ORCIDČíslo článku 132845 Zdroj.dok. Physica. D. - : Elsevier - ISSN 0167-2789
Roč. 418, Apr (2021)Poč.str. 12 s. Jazyk dok. eng - angličtina Země vyd. NL - Nizozemsko Klíč. slova Lévy processes ; Lévy-driven Ornstein–Uhlenbeck ; Non-Gaussian Ornstein–Uhlenbeck ; Ornstein–Uhlenbeck-Gamma proces ; Ornstein–Uhlenbeck-inverse Gaussian proces ; single neuron modelling Vědní obor RIV BD - Teorie informace Obor OECD Applied mathematics CEP GF20-21030L GA ČR - Grantová agentura ČR Způsob publikování Omezený přístup Institucionální podpora FGU-C - RVO:67985823 UT WOS 000624916700001 EID SCOPUS 85099921523 DOI https://doi.org/10.1016/j.physd.2021.132845 Anotace Shot noise processes have been extensively studied due to their mathematical properties and their relevance in several applications. Here, we consider nonnegative shot noise processes and prove their weak convergence to Lévy-driven Ornstein–Uhlenbeck (OU) process, whose features depend on the underlying jump distributions. Among others, we obtain the OU-Gamma and OU-Inverse Gaussian processes, having gamma and inverse gaussian processes as background Lévy processes, respectively. Then, we derive the necessary conditions guaranteeing the diffusion limit to a Gaussian OU process, show that they are not met unless allowing for negative jumps happening with probability going to zero, and quantify the error occurred when replacing the shot noise with the OU process and the non-Gaussian OU processes. The results offer a new class of models to be used instead of the commonly applied Gaussian OU processes to approximate synaptic input currents, membrane voltages or conductances modelled by shot noise in single neuron modelling. Pracoviště Fyziologický ústav Kontakt Lucie Trajhanová, lucie.trajhanova@fgu.cas.cz, Tel.: 241 062 400 Rok sběru 2022 Elektronická adresa https://doi.org/10.1016/j.physd.2021.132845
Počet záznamů: 1