Course Category：Professional Basic Course
Aims & Requirements：
This course is intended for graduate students of mathematical sciences, while can also serve as an elective for students from areas like management sciences. Stochastic Operations Research has wide applications and rich content. This course mainly focuses on designing and optimizing stochastic models. Particularly, given a realistic problem in this area, we would talk about how to model and analyze it in order to solve it. By addressing that, this course can help students lay foundation for further research and solving realistic problems.
Chapter 1 Renewal Process and its Applications
Definition of Renewal Process, extreme behaviors, renewal reward theorem, application of renewal theory in queuing theory, reliability, stochastic storage.
Chapter 2 Principle of Stochastic Dynamics
In cases of discrete and continuous time,, Finite time stochastic dynamics principles under discount criterion, infinite time stochastic dynamics principles, stochastic dynamics principles under average criterion.
Chapter 3 Stochastic Comparison
Various definitions of stochastic sequences, properties of some closure operations, applications of stochastic comparison in queuing theory, decision theory, stochastic storage.
 Ross S.M. Introduction to Probability Models, San Diego, CA. Academic Press, 1989.
 Ross S.M. Stochastic Processes, Wiley, New York, Second Edition, 1996.
 Shaked M. and J.G. Shanthikumar, Stochastic Orders, Springer, 2007.
Author：Hanqin Zhang (Academy of Mathematics and Systems Science)