摘要
综述随机偏微分方程的基本概念、理论、方法与应用,内容包括Hilbert空间中的Wiener过程、Ito随机积分、随机偏微分方程的解及其有效动力学。还介绍了随机偏微分方程的粗糙轨道、正则结构以及在Kardar-ParisiZhang(KPZ)方程中的应用。还介绍了段金桥与王伟的著作《Effective Dynamics of Stochastic Partial Differential Equations(随机偏微分方程的有效动力学)》的基本内容。
This is a survey and review about stochastic partial differential equations.This includes basic concepts,theory,methods and applications.More specifically,this article discusses Wiener process and It^ostochastic integral in Hilbert space,stochastic partial differential equations and their effective dynamics,rough paths and regularity structures.At the same time,an overview about the new book'Effective Dynamics of Stochastic Partial Differential Equations'(by Jinqiao Duan and Wei Wang)is provided.
出处
《数学建模及其应用》
2016年第2期1-8,共8页
Mathematical Modeling and Its Applications
基金
国家自然科学基金项目(11531006
11371367
11271290)
中央高校基本科研业务费专项资金(2014QT005)
