Shot noise, weak convergence and diffusion approximations
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Shot noise, weak convergence and diffusion approximations
Original language description
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.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GF20-21030L" target="_blank" >GF20-21030L: Stochastic models and methods for the study of olfaction</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Physica. D
ISSN
0167-2789
e-ISSN
1872-8022
Volume of the periodical
418
Issue of the periodical within the volume
Apr
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
12
Pages from-to
132845
UT code for WoS article
000624916700001
EID of the result in the Scopus database
2-s2.0-85099921523