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The limit distribution of inhomogeneous Markov processes and Kolmogorov’s problem

At the invitation of the school of mathematics science of Nanjing Normal University, Professor Zhenxin Liu, Professor of Dalian University of Technology, conducted an online academic exchange in the school of science and technology of our university on the morning of July 1, 2020, and made the topic "The limit distribution of inhomogeneous Markov processes and Kolmogorov’s problem" in the conference room 526 of the Xingjian building. Professor Hongjun Gao of the school of mathematics science presided over the report meeting, and some teachers of the school of mathematics science, masters and doctoral students of Applied Mathematics participated in the report meeting.

Professor Zhenxin Liu, professor and doctoral supervisor of School of Mathematical Sciences, Dalian University of Technology. He received his Ph.D. degree from Jilin University in 2007. In 2017, he was selected into the "Xinghai Jieqing" Talent Project of Dalian University of Technology, and won the National Outstanding Youth Science Fund in 2019. He mainly engaged in the research of stochastic analysis, stochastic differential equations and stochastic dynamical systems, paying special attention to the impact of random disturbance on the recurrence and stability of random dynamical systems. Part of the work was published in the internationally renowned mathematics magazine.

Professor Liu's report is divided into two parts. First, the first part discusses the limit distribution of non-homogeneous Markov processes generated by SDE. For this, Professor Liu introduced the homogeneous Markov processes and non-homogeneous Markov processes. Relevant properties and dynamic behaviors, and the limit distribution of the Markov process generated by SDE in aligned and non-homogeneous cases are visually compared by two figures. In the second part, Professor Liu introduced his recent works on the problem of Kolmogorov in the limit case of stationary distribution. First, what was the Kolmogrov problem was discussed, and then Professor Liu gave a detailed account of the work and difficult points made on the problem.

At the end of the talk, the students and teachers here put forward their own questions about the contents of the talk, and Professor Liu gave the answers with more details. The seminar had a complete success in the warm applause of teachers and students.