0541564 - FGÚ 2022 RIV NL eng J - Journal Article
Tamborrino, M. - Lánský, Petr
Shot noise, weak convergence and diffusion approximations.
Physica. D. Roč. 418, Apr (2021), č. článku 132845. ISSN 0167-2789. E-ISSN 1872-8022
R&D Projects: GA ČR(CZ) GF20-21030L
Institutional support: RVO:67985823
Keywords : Lévy processes * Lévy-driven Ornstein–Uhlenbeck * Non-Gaussian Ornstein–Uhlenbeck * Ornstein–Uhlenbeck-Gamma proces * Ornstein–Uhlenbeck-inverse Gaussian proces * single neuron modelling
OECD category: Applied mathematics
Impact factor: 3.751, year: 2021 ; AIS: 0.952, rok: 2021
Method of publishing: Limited access
Result website:
https://doi.org/10.1016/j.physd.2021.132845DOI: https://doi.org/10.1016/j.physd.2021.132845

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.
Permanent Link: http://hdl.handle.net/11104/0319105