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Stable and Gaussian Fluctuation Limit of a Lévy-Driven Slow-Fast System with Polynomial Dissipation
Abstract
We study fluctuation limit of a slow-fast system driven by α-stable Lévy noise with 1<α<2. The slow component is generated by an odd polynomial function f(y):=yq, while in the fast component, the drift is g(y):=−|y|psgn(y) for some p>0. Although the noise is given, the fluctuation limit is either a stable process or a Brownian motion, depending on both p and α. The critical line between stable limit and Brownian limit is q+1−p=α/2.
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BibTeX
@misc{zhao2026stable,
title = {{Stable and Gaussian Fluctuation Limit of a Lévy-Driven Slow-Fast System with Polynomial Dissipation}},
author = {Qingming Zhao and Xueru Liu and Wei Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09906},
eprint = {2609.09906},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09906},
}
RIS
TY - UNPB
TI - Stable and Gaussian Fluctuation Limit of a Lévy-Driven Slow-Fast System with Polynomial Dissipation
AU - Qingming Zhao
AU - Xueru Liu
AU - Wei Wang
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.09906
UR - https://arxiv.org/abs/2609.09906
AB - We study fluctuation limit of a slow-fast system driven by α-stable Lévy noise with 1<α<2. The slow component is generated by an odd polynomial function f(y):=y^q, while in the fast component, the drift is g(y):=−|y|^psgn(y) for some p>0. Although the noise is given, the fluctuation limit is either a stable process or a Brownian motion, depending on both p and α. The critical line between stable limit and Brownian limit is q+1−p=α/2.
ER -