带多项式耗散的Lévy驱动慢快系统的稳定与高斯波动极限
Stable and Gaussian Fluctuation Limit of a Lévy-Driven Slow-Fast System with Polynomial Dissipation
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- School of Mathematics, Nanjing University（南京大学数学系）
- School of Mathematical Sciences, Dalian University of Technology（大连理工大学数学科学学部）
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中文总结 AI 辅助
本文研究由α-稳定Lévy噪声驱动的慢快系统的波动极限，发现极限类型（稳定过程或布朗运动）由参数p和α决定，临界线为q+1-p=α/2。
中文摘要 AI 辅助
我们研究了由$1<\alpha<2$的$\alpha$-稳定Lévy噪声驱动的慢快系统的波动极限。慢分量由奇多项式函数$f(y):=y^q$生成，而快分量中的漂移为$g(y):=-|y|^p\operatorname{sgn}(y)$，其中$p>0$。尽管噪声是给定的，波动极限要么是稳定过程，要么是布朗运动，这取决于$p$和$\alpha$两者。稳定极限与布朗极限之间的临界线为$q+1-p=\alpha/2$。
英文摘要
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 $g(y):=-|y|^p\operatorname{sgn}(y)$ 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 $q+1-p=α/2.$
