Small mass limit for stochastic interacting particle systems with Lévy noise and linear alignment force.
Chaos
; 34(2)2024 Feb 01.
Article
em En
| MEDLINE
| ID: mdl-38416671
ABSTRACT
We study the small mass limit in mean field theory for an interacting particle system with non-Gaussian Lévy noise. When the Lévy noise has a finite second moment, we obtain the limit equation with convergence rate ε+1/εN, by taking first the mean field limit Nâ∞ and then the small mass limit εâ0. If the order of the two limits is exchanged, the limit equation remains the same but has a different convergence rate ε+1/N. However, when the Lévy noise is α-stable, which has an infinite second moment, we can only obtain the limit equation by taking first the small mass limit and then the mean field limit, with the convergence rate 1/Nα-1+1/Np2+εp/α where p∈(1,α). This provides an effectively limit model for an interacting particle system under a non-Gaussian Lévy fluctuation, with rigorous error estimates.
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01-internacional
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MEDLINE
Idioma:
En
Ano de publicação:
2024
Tipo de documento:
Article