Approximation for random stable manifolds under multiplicative correlated noises
Approximation for random stable manifolds under multiplicative correlated noises
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DOI：
10.3934/dcdsb.2016091
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发表时间：
2016-10
影响因子：
1.2
通讯作者：
Tao Jiang;Xianming Liu;Jinqiao Duan
中科院分区：
文献类型：
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作者：
Tao Jiang;Xianming Liu;Jinqiao Duan
通常的Wong-Zakai近似是关于模拟随机微分方程（SDEs）的个体解。从动力系统的角度来看，它也是有趣的近似随机不变流形，这是几何对象有用的理解如何复杂的动态随机影响下演变。研究了带乘性相关噪声的随机发展方程的随机稳定流形的Wong-Zakai型逼近。基于解在不变流形上的收敛性，我们用一族带有光滑相关噪声的扰动随机系统的不变流形来逼近随机稳定流形（即，集成的Ornstein-Uhlenbeck工艺）。这种近似的收敛性。
The usual Wong-Zakai approximation is about simulating individual solutions of stochastic differential equations(SDEs). From the perspective of dynamical systems, it is also interesting to approximate random invariant manifolds which are geometric objects useful for understanding how complex dynamics evolve under stochastic influences. We study a Wong-Zakai type of approximation for the random stable manifold of a stochastic evolutionary equation with multiplicative correlated noise. Based on the convergence of solutions on the invariant manifold, we approximate the random stable manifold by the invariant manifolds of a family of perturbed stochastic systems with smooth correlated noise (i.e., an integrated Ornstein-Uhlenbeck process). The convergence of this approximation is established.