UWO, Department of Statistical and Actuarial Sciences,

Stat. 452b: Stochastic Processes

Course Outline

 

  Instructor: Zinovi Krougly, WSC 223, (519) 661-2111 ext. 88232, email: zkrougly@stats.uwo.ca

  Course Schedule: MW  4:00 - 5:30p.m., WSC 240

  Office Hours: MW  2:00 - 3:30 p.m. or by appointment. 

 

 TEXT:  1. Sheldon M. Ross, Introduction to Probability Models by, 6th (or 7th) edition.

 REFERENCES:

  2.   P. C. Edward Kao, An Introduction to Stochastic Processes, Duxbury Press, 1997.

  3.   R. Nelson, Probability, Stochastic Processes, and Queueing Theory, Springer-Verlag, 1995.

4.      A. O. Allen. Probability, Statistics, and Queuing Theory with Computer Science Applications. Academic Press, 1990.

5.      R. Durrett. Essentials of Stochastic Processes, Springer-Verlag, 1999.

6.      J. P. Buzen. Computational algorithms for closed queueing networks with exponential servers, Comm. ACM, 16(9), 1973,  527-531.

7.      S.C. Bruell and G. Balbo. Computational Algorithms for Closed Queueing Networks. North-Holland, 1980.

 

COURSE DESCRIPTION:

Renewal Theory, Brownian Motion, Queuing Theory (Queueing Networks). 

These topics are covered in chapters 7, 8, 10 of the text and the references.       

3 assignments (every 6 8 questions, or programming assignments)

Stochastic Processes is a very large field, and we will try to cover the important techniques, mathematical strength and computational algorithms (programming examples and assignments). We will study Renewal Processes, Brownian Motion, Queueing Network Models. If time allows, we may also address more advanced topics and examples, like Computational Algorithms and Performance Formulas for Markovian Queueing Networks, Decomposition and Approximation Methods. I will give necessary examples in financial and computer science applications using analytical and simulation models, like Database Degradation Model, the Pricing Stock Options and Black-Scholes Formula, Multiprogramming Models, Computer Performance Models.

The course contains mathematical problems and computer exercises. Students will be expected to write and execute programs pertinent to the material of the course. No programming experience is necessary or assumed. But the willingness to accept a computer as a tool is a requirement.

I will attempt to answer technical questions and provide examples, using Mathematica, MATLAB, C++. C/C++ programming language is one of the most powerful. MS Visual Basic 6, Visual Basic for Application in Windows or QBASIC 4.5 on IBM-compatible PC is perhaps the easiest programming language to learn. Visual Fortran in Windows is also available in our department. Other programming languages (R, SAS, S-Plus, Excel, etc.) also can be used.

 

GRADING:

Choice A = 30% Midterm Exam + 40% Final Exam + 30% Assignments (incl. Programming Assignments)

Choice B = 35% Midterm Exam + 50% Final Exam + 15%Assignments (incl. Programming Assignments)

 

The grading for the course will be Max {A, B}

 

There will be 3 assignments. The final exam will consist of a three-hour exam.