报 告 人: Michael Röckner 教授

报告题目:A natural extension of Markov processes and applications to singular SDEs





sb沙巴体育官方投注   Michael Röckner教授是国际著名的数学家,目前担任德国数学会主席、德国DFG基金评审委员会委员(40名委员中唯一一位数学委员)、德国洪堡基金评审委员、欧盟科学研究委员会(ERC)前沿基金评审委员会数学部主席(Chair of the Mathematics Panel)、德国Bielefeld大学ZIF交叉科学研究中心主任以及Bielefeld大学数学系系主任,中国科学院国家“千人计划”专家。

  Michael Röckner教授在概率统计及相关领域科研成果卓著,目前已出版专著5本,在概率统计等领域顶级期刊CPAM、CMP、AOP、PTRF、JFA等发表高水平SCI论文320余篇,论文引用次数超过4000次(2002年ISI Web of Knowledge评选的世界高引科学家Michael Röckner教授在数学家中全球排名第三)。 Michael Röckner教授曾荣获Max-Planck Research Prize、Sir Edmund Whittaker Memorial Prize、Heinz–Mayer–Leibnitz Prize等多个国际数学/科学奖,目前担任包括概率统计顶级期刊Annals of Probability在内的9个高水平SCI期刊编委和8个国际会议Proceeding编委, 现/曾主持多个重大国际合作项目(包括与美国、俄罗斯、意大利、澳大利亚、波兰、罗马利亚、乌克兰、日本、中国及欧盟等合作项目)。


  We develop a general method for extending Markov processes to a larger state space such that the added points form a polar set.  The so obtained extension is an improvement on the standard trivial extension in which case the process is made stuck in the added points, and it renders a new technique of constructing extended solutions to S(P)DEs from all starting points, in such a way that they are solutions at least after any strictly positive time. Concretely, we adopt this strategy to study SDEs with singular coefficients on an infinite dimensional state space (e.g. SPDEs of evolutionary type), for which one often encounters the situation where not every point in the space is allowed as an initial condition. The same can happen when constructing solutions of martingale problems or Markov processes from (generalized) Dirichlet forms, to which our new technique also applies. Joint work with:Lucian Beznea (Romanian Academy, Bucharest, Romania),Iulian Cîmpean (Romanian Academy, Bucharest, Romania).