主講人：GeorgeYin
講座題目：Switching Diffusion Systems and Applications
時　　間：2012年7月23，24，25，26，27日上午9：00~10:20
地　　點：研究生樓209A
主講人介紹
　　GeorgeYin received the B.S. degree in mathematics (magna cum laude) from the University of Delaware in 1983, and M.S. degree in Applied Mathematics in 1984 and another M.S. degree in electrical engineering in 1987, both from Brown University. He received his Ph.D. degree in Applied Mathematics from Brown University in 1987. Since August 2011, he has been a Professor at the Department of Mathematics at Wayne State University,Detroit, since 1996.
　　His research interests include Applied probability and stochastic processes, stochastic approximation and optimization, singular perturbation, numerical methods in stochastic systems, mathematics of finance, manufacturing systems, signal processing, communication network, estimation and system identification, stochastic control, stochastic systems theory.George Yin is a prolific researcher, who has authored more than 270 papers. His papers appeared in top journals, and some of them are highly cited.
　　He is an elected (in 2002) IEEE fellow. He received Charles H. Gershenson Distinguished Faculty Fellowship in 2001 and Distinguished Graduate Faculty Award in 2011 from Wayne State University, 2011. He currently serves as the Vice President of Academy of Scholars at Wayne State University,
主要內容：
　　Numerous problems in control and optimization require the treatment of systems in which continuous dynamics and discrete events coexist. The discrete component is given by a random jump process with a finite state space, and the continuous component is the solution of a stochastic differential equation. Seemingly similar to diffusions, the processes have a number of salient features distinctly different from diffusion processes. After providing motivational examples arising from wireless communications, identification, finance, singular perturbed Markovian systems, manufacturing, and consensus controls, we present necessary and sufficient conditions for positive recurrence, study ergodicity,investigate stability and stabilization, and discuss related problems
arising in numerical solutions of differential equations,control, and game problems.

A Note: In the lectures, I will try to give presentations that will be accessible to graduate students. The main effort is to provide an overview but not to be heavily technical.

Some related references

R.Z. Khasminskii, C. Zhu, and G. Yin,
Stability of regime-switching
diffusions, Stochastic Processes and Their
Applications, 117 (2007), 1037--1051.

X. Mao and C. Yuan, Stochastic Differential Equations with
Markovian Switching, Imperial College Press, London, UK, 2006.

G. Yin and C. Zhu,
Hybrid Switching Diffusions: Properties and Applications,Springer, New
York, 2010, [Stochastic Modeling and Applied Probability, Volume63].