Slow manifolds for stochastic systems with non-Gaussian stable L\'evy noise
Abstract
This work is concerned with the dynamics of a class of slow-fast stochastic dynamical systems with non-Gaussian stable L\'evy noise with a scale parameter. Slow manifolds with exponentially tracking property are constructed, eliminating the fast variables to reduce the dimension of these coupled dynamical systems. It is shown that as the scale parameter tends to zero, the slow manifolds converge to critical manifolds in distribution, which helps understand long time dynamics. The approximation of slow manifolds with error estimate in distribution are also considered.
Keywords
Cite
@article{arxiv.1702.08213,
title = {Slow manifolds for stochastic systems with non-Gaussian stable L\'evy noise},
author = {Shenglan Yuan and Jianyu Hu and Xianming Liu and Jinqiao Duan},
journal= {arXiv preprint arXiv:1702.08213},
year = {2017}
}
Comments
35 pages, 6 figures. The authors are grateful to Bj\"orn Schmalfu{\ss}, Ren\'e Schilling, Georg Gottwald, Jicheng Liu and Jinlong Wei for helpful discussions on stochastic differenial equations driven by L\'evy motions