Random invariant manifolds of stochastic evolution equations driven by Gaussian and non-Gaussian noises

被引：0
|
作者：
Liu, Xianming [1 ]
机构：
[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China
来源：
JOURNAL OF MATHEMATICAL PHYSICS | 2021年 / 62卷 / 11期
关键词：
APPROXIMATION;
D O I：
10.1063/5.0065640
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
The goal of this work is to compare the invariant manifold of the stochastic evolution equation driven by an alpha-stable process with the invariant manifold of the stochastic evolution equation forced by Brownian motion. First, we show that the solution of the Marcus stochastic evolution equation driven by a type of alpha-stable process converges to the solution of the related Stratonovich stochastic evolution equation forced by Brownian motion. Then, we study the invariant stable manifold of the stochastic evolution equation driven by an alpha-stable process. Finally, we prove that the invariant stable manifold of the Marcus stochastic evolution equation driven by an alpha-stable process converges in probability to the invariant stable manifold of the Stratonovich stochastic evolution equation forced by Brownian motion. The connection between the random dynamical system driven by non-Gaussian noise and the random dynamical system driven by Gaussian noise is established.</p>
引用
收藏
页数：20
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