Electron. J. Differential Equations,
Vol. 2019 (2019), No. 68, pp. 1-21.
Invariant foliations for stochastic dynamical systems
with multiplicative stable Levy noise
Ying Chao, Pingyuan Wei, Shenglan Yuan
Abstract:
This work concerns the dynamics of a class of stochastic dynamical systems
with a multiplicative non-Gaussian Levy noise. We first establish the
existence of stable and unstable foliations for this kind of system via the
Lyapunov-Perron method. Then we examine the geometric structure of the
invariant foliations, and their relation with invariant manifolds.
Also we illustrate our results in an example.
Submitted August 10, 2018. Published May 14, 2019.
Math Subject Classifications: 60H10, 37D10, 37H05.
Key Words: Stochastic differential equation; random dynamical system;
invariant foliation; invariant manifold; geometric structure.
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Ying Chao
School of Mathematics and Statistics and Center for Mathematical Sciences
Hubei Key Laboratory of Engineering Modeling and Scientific Computing
Huazhong University of Sciences and Technology
Wuhan 430074, China
email: yingchao1993@hust.edu.cn
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Pingyuan Wei
School of Mathematics and Statistics and Center for Mathematical Sciences
Hubei Key Laboratory of Engineering Modeling and Scientific Computing
Huazhong University of Sciences and Technology
Wuhan 430074, China
email: weipingyuan@hust.edu.cn
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Shenglan Yuan
School of Mathematics and Statistics and Center for Mathematical Sciences
Hubei Key Laboratory of Engineering Modeling and Scientific Computing
Huazhong University of Sciences and Technology
Wuhan 430074, China
email: shenglanyuan@hust.edu.cn
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