Approximate the dynamical behavior for stochastic systems by Wong-Zakai approaching

作者：Guo, Zhongkai; Yan, Xingjie^*; Wang, Weifeng; Liu, Xianming

来源：Journal of Mathematical Analysis and Applications, 2018, 457(1): 214-232.

DOI：10.1016/j.jmaa.2017.08.004

• Stochastic partial differential equation
• Invariant manifolds
• Invariant foliations
• Wong-Zakai approximation

Random invariant manifolds and foliations play an important role in the study of the qualitative dynamical behaviors for nonlinear stochastic partial differential equations. In a general way, these random objects are difficult to be visualized geometrically or computed numerically. The current work provides a perturbation approach to approximate these random invariant manifolds and foliations. After briefly discussing the existence of random invariant manifolds and foliations for a class of stochastic systems driven by additive noises, the corresponding Wong-Zakai type of convergence result in path-wise sense is established.

• 出版日期2018-1-1
• 单位中南民族大学; 中国矿业大学（北京）; 华中科技大学