讲座题目：Mass Distribution in Stochastic Flow: Asymptotics and Analysis - 2021寒假吉大学子全球胜任力提升计划（线上项目）
报 告 人：Andrii Dorohovtsev, Professor, National Academy of Sciences of Ukraine
报告地点：Zoom 会议号: 843 4366 4410 密码：1
校内联系人：韩月才 hanyc@jlu.edu.cn
讲座内容及时间（北京时间）安排：
授课日期 |
课程名称（讲座题目） |
授课时间 |
2021-2-3 |
Generalized functionals from Gaussian random fields. |
16:00-17:00 |
2021-2-5 |
Local nondeterminism and self-intersection local times for Gaussian random fields. Self-intersection local times under the transformation of the field. |
16:00-17:00 |
2021-2-10 |
Integral curvatives, small tube asymptotic and Le Gall formula. |
16:00-17:00 |
2021-2-17 |
Random surface in the flow with interaction. |
16:00-17:00 |
2021-2-19 |
Clark-Ocone formula for random variables. |
16:00-17:00 |
2021-2-24 |
Clark representation for random measures. |
16:00-17:00 |
2021-2-26 |
Clark representation for random surfaces |
16:00-17:00 |
讲座摘要：We consider motion of non-smooth curves and surfaces in random media. One of the main sources for problems under consideration is mathematical theory of polymers, where the polymers are described as the random curves or surfaces which are non-smooth. In the lectures we discuss following two questions. How the geometry of non-smooth surface can be described and how it changes with the time in the stochastic flow. We propose to describe the surface in the finite-dimensional space by its visitation measure. Instead of Lipschitz-Killing curvatures we use the self-intersection local times formally defined as the multiple integrals from the delta function with respect to visitation measure. The visitation measure can be treated as a mass distribution for the system of particles. We describe its motion with the help of stochastic flow with interaction. In the lectures we discuss the asymptotic properties and structure of the obtained measure-valued process.
报告人简介：Andrii Dorohovtsev教授是乌克兰国家科学院数学所随机过程理论系主任，主要从事概率论及其相关领域研究，是乌克兰概率论研究方向学术领军人物之一。Andrii教授是乌克兰与德国、乌克兰与俄罗斯等国家联合项目的乌方负责人。同时，Andrii Dorohovtsev教授是《Theory of Stochastic Processes》、《UKraine Mathematical Journal》等杂志的编委。
