摘要：In this talk, firstly I will briefly introduce the notion, Lyapunov criteria and stabilization methods of finite-time stability for stochastic nonlinear systems, and then a new Lyapunov theorem of stochastic finite-time stability is proposed, and it shows that this new Lyapunov theorem not only is a generalization of classical stochastic finite-time theorem, but also reveals the important role of white-noise in finite-time stabilizing stochastic systems. In order to overcome limitations of finite-time stochastic stability, a novelty domain stability for stochastic nonlinear systems is considered, which is formulated and analyzed in terms of the residence probability measure. The regularity of stochastic differential equations needs to be considered, and an extended existence and uniqueness theorem is proven by using Khasminskii's criteria. Some sufficient conditions for recurrence are proposed to derive upper bounds of mean residence time. In particular, under certain conditions, a connection between the mean of residence time and the Dirichlet problem has been built; accordingly, numerical methods can be used to solve the mean of the residence time. At last, for some controlled stochastic systems, suitable admissible controllers can be designed for the purpose of domain aiming control.

个人简介：尹居良，广州大学“百人计划”特聘教授，统计学专业博士生导师，澳大利亚Deakin大学荣誉教授，广东省高校“千百十工程”第四批培养人才。2003年毕业于中山大学数学学院概率论与数理统计专业，获理学博士学位，2003年-2005年在南开大学数学学院作博士后研究。1997年-2017年在暨南大学工作，2009年晋升教授，2011年遴选为统计学专业和数量经济学专业博士生导师，2013年被评为暨南大学杰出青年学者。曾任广东省现场统计协会秘书长和常务理事。主要从事随机分析与随机控制、数理金融与保险精算、时间序列分析等领域的教学与研究工作。迄今为止，参编、参撰教材和著作各1部，先后主持省部级科研项目7项、国家自然科学基金项目2项，正式发表各类学术论文近50篇，其中被SCI和SSCI索引收录近30篇，有2篇入选ESI高被引论文。2007年和2008年分别获广东省统计科学研究成果一等奖和全国优秀统计成果三等奖。

主持人：李韬 教授