马氏过程研讨会

发布时间:2019年11月26日 作者:刘源远   消息来源:    阅读次数:[]

系列学术报告

1.报告题目:Stochastic Damping Hamiltonian Systems with State-Dependent Switching

报告时间:2019.11.30(星期六)上午8:20-9:00

报告地点:数理楼135

报告摘要:This work focuses on a class of stochastic damping Hamiltonian systems with state-dependent switching, where the switching process has a countably infinite state space. First, the existence and uniqueness of a global weak solution is constructed by the martingale approach on the basis of that only weak solution to each subsystem is available. Then, strong Feller property is proved by the killing technique together with the resolvent and transition probability identities. This approach relaxes the continuity assumption for the switching rates $q_{kl}(\cdot)$ commonly used in the literature to merely measurable. Next, exponential ergodicity is obtained under a Foster-Lyapunov drift condition. Finally, a regime-switching van der Pol system is studied for illustration. This is a joint work with Fuke Wu and Chao Zhu.

报告人简介:席福宝,北京理工大学数学与统计学院教授,博士生导师;主要从事马氏过程与随机分析领域的研究;特别地,关于含小参数的切换扩散过程的大偏差,关于切换跳扩散过程的随机稳定性、Feller性、强Feller性、指数遍历性、强遍历性以及收敛速度估计等方面,取得了一系列重要研究成果;部分论文发表在SIAM Journal on Control and Optimization, Stochastic Processes and their Applications, Journal of Differential Equations, Journal of Applied Probability, Science China Mathematics等国内外重要学术期刊上。

2. 报告题目:Potential theory for asymmetric Markov chains

报告时间:2019.11.30(星期六)上午9:00-9:40;

报告地点:数理楼135

报告摘要:I will review the potential theory for Markov chains and report some new progress on the variational principle for hitting times and capacity for asymmetric Markov chains. Some applications and comparison theorems are obtained.

报告人简介:毛永华,男,北京师范大学教授,博士生导师。从事Markov遍历理论和相关理论研究及其应用。入选教育部新世纪优秀人才计划,参加了国家自然科学创新群体项目3项,973项目2项,及主持青年基金和面上基金各1项等。现为国际SCI刊物《Statistics and Probability Letters》编委。

3. 报告题目:Moments of integral-type functional downward for single death processes

报告时间2019.11.30(星期六)上午9:40-10:20;

报告地点:数理楼135

报告摘要In this talk, we present an explicit and recursive representation for high order moments of integral-type functional downward for single death processes. This talk is based on the joint work with Jing Wang.

报告人简介:张余辉, 生于1968年,教授,博士生导师。1990年本科毕业于北京大学概率论与数理统计系,1993年硕士毕业于北京师范大学数学系,师从严士健和刘秀芳教授,1996年博士毕业于北京师范大学数学系并留系工作,导师为陈木法院士, 2004年被聘任为教授。2004年至2008年任数学科学学院副院长,2013年至2017年任教育部高等学校大学数学课程教学指导委员会委员。2009年评为北京市优秀教师。主要从事随机过程及交叉领域的理论研究,包括交互作用无穷粒子系统马氏过程、跳过程的稳定性理论、耦合方法、对偶方法,泛函不等式和特征值估计等,特别是对单生过程有较完整的研究,目前的主要研究兴趣是单死过程的稳定性理论。先后访问过俄罗斯、法国、德国、英国、中国台湾等10余所科研院所和大学。主持国家自然科学基金青年项目和面上项目各1项,参加国家自然科学基金创新研究群体项目、重点项目、科技部973项目和教育部高校博士点基金项目等多项。

茶歇 10:20-10:40 学术交流室

4. 报告题目:Risk-sensitive finite-horizon piecewise deterministic Markov decision processes

报告时间2019.11.30(星期六)上午10:40-11:20;

报告地点:数理楼135

报告摘要:This talk discussed risk-sensitive piecewise deterministic Markov decision processes, where the expected exponential utility of a finite-horizon reward is to be maximized. Both the transition rates and reward functions are allowed to be unbounded. The Feynman-Kac's formula is developed in our setup, using which along with an approximation technique, we establish the associated Hamilton-Jacobi-Bellman equation and the existence of risk-sensitive optimal policies under suitable conditions.

报告人简介:黄永辉,中山大学数学学院副教授,硕士生导师。2010年6月获中山大学博士学位,2010年7月至2013年12月任中山大学讲师,2014年1月至今任中山大学副教授。主要研究方向为马尔可夫决策过程和随机博弈,在概率论和运筹学主流期刊 《Adv. Appl. Probab.》、《Stochastic》、《SIAM J. Optim.》、《European. J. Oper. Res.》、《Math. Oper. Res.》等发表论文10余篇。

5.报告题目: Long time behavior of Lévy-driven Ornstein-Uhlenbeck process with regime-switchin

报告时间2019.11.30(星期六)上午11:20-12:00;

报告地点:数理楼135

报告摘要:In this work we investigate the long time behavior of the Ornstein-Uhlenbeck process driven by Lévy noise with regime-switching. We provide explicit criteria on the transience and recurrence of this process. Contrasted with the Ornstein-Uhlenbeck process driven simply by Brownian motion, whose stationary distribution must be light-tailed, both the jumps caused by the Lévy noise and regime-switching described by Markov chain can derive the heavy-tailed property of the stationary distribution. In this work, the different role played by Lévy measure and regime-switching process is clearly characterized.

报告人简介:廖仲威,华南师范大学华南数学应用与交叉研究中心研究员。2016年毕业于北京师范大学,师从陈木法院士。毕业后于中山大学数学学院从事专职科研副研究员。研究兴趣包括:随机控制,马氏过程遍历性等。目前主要工作在随机控制与最优化理论,工作发表于SIAM J. Control Optim., J.Optim. Theory Appl. J. Appl. Prob.Adv. Nonlinear Studies

 



打印】【收藏】 【关闭