报 告 人：鲍建海 副教授
报告题目：A strong limit theorem for two-time-scale SPDEs
报告时间：2015 年12月 16日（周三）下午4：00
报告地点：静远楼1506学术报告厅
主办单位：数学与统计学院、科技处
摘 要： This paper focuses onSPDEs under two –time -scale formulation.
Distinct from the work in the existing literature,the systems are driven by-table processes with.In addition, the SPDEs are either modulated by a continuous time Markov chain or have an addition fast jump component.
The inclusion of the Markov chain is for the needs of treating random environment, whereas the addition of the fast jump process enables the consideration of discontinuity in the sample paths of the fast processes. Assuming either a fast changing Markov switching or an additional fast-varying jump process, this work aims to obtain the averaging principles for such systems.There are several distinct difficulties. First, the noise is not square integrable. Second, in our setup, for the underlying SPDE,there is only a unique mild solution and as a result, there is no’s formula that can be used.Moreover, another new aspect is the addition of the fast regime switching and the addition of the fast varying jump processes in the formulation, which enlarges the applicability of the underlying systems. To overcome these difficulties, a semigroup approach is taken. Under suitable conditions, it is proved that the pth moment convergence takes place withuniformly, which is stronger than the usual weak convergence approaches. In addition, certain error bounds are also obtained.
鲍建海副教授简介：
鲍建海，山东微山县人，现为中南大学数学与统计学院副教授，主要研究领域：随机分析，泛函随机微分方程，马氏切换随机微分方程.
2004年07月毕业于曲阜师范大学数学院的应用数学专业，获学士学位；2007年3月毕业于中南大学数学与统计学院的概率论与数理统计专业，获硕士学位；2011年08月毕业于中南大学数学与统计学院的概率论与数理统计专业，获博士学位；2013年01月毕业于英国斯旺西大学(Swansea University)的概率论与数理统计专业，获博士学位；2012年09月---2013年08月在美国韦恩州立大学(Wayne State University) 从事 Research Fellow.
先后在Stoch.Proc.Appl.，Bernoulli,Electron. J. Probab.,J. Theoret. Probab.,Potential Anal.,SIAM J. Control Optim.,SIAM J. Appl. Math. 等期刊上发表20余篇学术论文