分数Brown运动是一类具有非半鞅性与非Markov性的Gauss过程，因而其诱导的随机动力系统的研究方法与传统随机分析的研究方法有本质的区别，需要建立新的数学理论框架。申请者计划从2021年6月28日至2021年7月16日在华南理工大学面向研究生、博士后、青年教师以及相关研究人员举办一个为期3周专题讲习班。我们将邀请美国杨百翰大学吕克宁教授、德国耶拿大学Björn Schmalfuss教授与西班牙塞维利亚大学María Garrido-Atienza等3位国际著名专家，系统详细地讲解分数Brown运动及其诱导的随机动力系统的数学理论，包括分数Brown运动的构造及性质、分数Brown运动驱动的随机（偏）微分方程的指数稳定性、随机动力系统、随机吸引子、不稳定流形及相关应用。期望本项目的开展对我国随机微分方程及其动力系统的相关领域的发展以及青年人才的培养起到重要的促进和推动作用。

The fractional Brownian motion is Gaussian process with the non-semimartingale property and non-Markov property, so there are essential differences between the approaches for its generated random dynamical systems and the classical stochastic analysis ones, resulting in building a new mathematical theoretical framework. In this project we plan to organize a three-week seminar for graduates, postdocs, young researchers and related researchers at South China University of Technology from June 28 to July 16 in 2021. We will invite Prof. Kening Lu from the Brigham Young University in United States, Prof. Björn Schmalfuss from the Friedrich-Schiller University of Jena in Germany and Prof. María J. Garrido-Atienza from the University of Seville in Spain to systematically present the mathematical theories of fractional Brownian motion and its induced random dynamical systems, including the construction and properties of fractional Brownian motion, the exponential stabilities, random dynamical systems, random attractors, unstable manifolds and related applications of the stochastic (partial) differential equations. And we expect that this project can play an important role in promoting the development of stochastic differential equations and their random dynamical systems and related fields in China and the cultivation of young talents.