Shot noise, weak convergence and diffusion approximations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985823%3A_____%2F21%3A00541564" target="_blank" >RIV/67985823:_____/21:00541564 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.physd.2021.132845" target="_blank" >https://doi.org/10.1016/j.physd.2021.132845</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.physd.2021.132845" target="_blank" >10.1016/j.physd.2021.132845</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Shot noise, weak convergence and diffusion approximations

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Shot noise, weak convergence and diffusion approximations

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GF20-21030L" target="_blank" >GF20-21030L: Stochastické modely a postupy pro studium olfakce</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Physica. D

ISSN

0167-2789

e-ISSN

1872-8022

Svazek periodika

418

Číslo periodika v rámci svazku

Apr

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

12

Strana od-do

132845

Kód UT WoS článku

000624916700001

EID výsledku v databázi Scopus

2-s2.0-85099921523