UWO, Department of
Statistical and Actuarial Sciences,

Stat. 452b: Stochastic
Processes

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, 6^{th} (or 7^{th})
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)

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