Workshop in Stochastic Differential Equations
主办单位：华中科技大学数学中心
时间：2015年12月19日至12月20日
地点：华中科技大学创新研究院恩明楼8楼
Speakers
Chenggui Yuan (Swansea University)
吴昭景 (烟台大学)
李晓月 (东北师范大学)
鲍建海 (中南大学)
史敬涛 (山东大学)
Organizers
段金桥(华中科技大学)
吴付科 (华中科技大学)
Schedule
2015,Dec 19
| Time
| Speaker
| Title
| 14:30–15:30
| 袁成桂
| Harnack inequality and exponential Integrability for FSDEs
| 15:30–16:30
| 吴昭景
| Analysis on input-to-state stability by mean transform inequality
| 2015,Dec 20
| Time
| Speaker
| Title
| 8:30–9:30
| 李晓月
| The Almost Sure Stability of Coupled Systems of Stochastic Differential System with Variable Delays on Networks
| 9:30–10:15
| 鲍建海
| Permanence and extinction of regime-switching predator-prey models
| 10:45–11:30
| 史敬涛
| Leader-Follower Stochastic Differential Game with Asymmetric Information and Applications
|
报告（一）
时间：2015年12月19日（星期六）14:30–15:30
地点：华中科技大学数学中心（创新研究院 恩明楼813）
报告人：袁成桂，Swansea University，副教授
报告题目： Harnack inequality and exponential integrability for FSDEs
报告摘要：In this talk, we will start with Wang’s Harnack inequality, we then move to the Harnack inequality of functional stochastic differential equations (FSDEs). The exponential integrability will be discussed by applying the theory of the Harnack equality.
报告（二）
时间：2015年12月19日（星期六）15:30–16:30
地点：华中科技大学数学中心（创新研究院 恩明楼813）
报告人：吴昭景，烟台大学 教授
报告题目：Analysis on input-to-state stability by mean transform inequality
报告摘要：To overcome the requirement on convexity of Jensen's inequality, for a stochastic process, a mean transform inequality is proposed, by which the mathematic expectation can be moved into a smooth comparison function. To reduce the conservatism of asymptotic-stable function and input-state gain function of stochastic input-to-state stability, the notion of input-to-state stability in the mean squire (ISS-2M) is presented. By the aid of mean transform inequality, the analysis on criteria of ISS-2M is performed as neatly as that in the deterministic case.
报告（三）
时间：2015年12月20日（星期日）8:30–9:30
地点：华中科技大学数学中心（创新研究院 恩明楼813）
报告人：李晓月，东北师范大学 教授
报告题目：The Almost Sure Stability of Coupled Systems of Stochastic Differential System with Variable Delays on Networks
报告摘要：We investigate the coupled systems of stochastic differential equations with variable delays (CSDDEs) on networks. We analyze existence and uniqueness of the global solution by combined method of graph theory and Lyapunov function analysis. Furthermore, we ultilize the graph theory technique and the nonnegative semi-martingale convergence theorem to obtain the almost sure stability of sample solutions and the sufficient principles to locate their limit sets, which correlate closely with the topology property of the CSDDEs. Finally we illustrate our main results by some examples.
报告（四）
时间：2015年12月20日（星期日）9:30–10:15
地点：华中科技大学数学中心（创新研究院 恩明楼813）
报告人：鲍建海，中南大学 副教授
报告题目：Permanence and extinction of regime-switching predator-prey models.
报告摘要：In this work we study the permanence and extinction of a regime-witching predatorprey model with Beddington-DeAngelis functional response. The switching process is used to describe the random changing of corresponding parameters such as birth and death rates of a species in different environments. When a prey will die out in some fixed environments and will not in others, our criteria can justify whether it dies out or not in a random switching environment. Our criteria are rather sharp, and they cover the known on-off type results on permanence of predator-prey models without switching. Our method relies on the recent study of ergodicity of regime-switching diffusion processes.
报告（五）
时间：2015年12月20日（星期五）10:45–11:30
地点：华中科技大学数学中心（创新研究院 恩明楼813）
报告人：史敬涛，山东大学 副教授
报告题目：Leader-Follower Stochastic Differential Game with Asymmetric Information and Applications
报告摘要：In this talk, we will discuss a leader-follower stochastic differential game with asymmetric information, where the information available to the follower is based on some sub-σ-algebra of that available to the leader. Such kind of game problem has wide applications in finance, economics and management engineering such as newsvendor problems, cooperative advertising and pricing problems. Stochastic maximum principles and verification theorems with partial information are obtained, to represent the Stackelberg equilibrium. As applications, a linear-quadratic leader-follower stochastic differential game with asymmetric information is studied. It is shown that the open-loop Stackelberg equilibrium admits a state feedback representation if some system of Riccati equations is solvable.
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