Math 357H: Introduction to Stochastic Processes

Fall 2007

Instructor:Michelle Boué Email:

michelleboue@trentu.caOffice Phone:748-1011 x7925 Office hours:

Monday 12-1 Tuesday 11-12 Friday 10-11 Office:Peter Gzowski College 332

Secretary:Carolyn Johns Email:math@trentu.caor cjohns@trentu.caOffice Phone:748-1011 x7531 Fax:748-1155 Office:Peter Gzowski College 341

COURSE TOPICSThe goal of this course is to present a variety of important models used in modeling of random events that evolve in time. These include Markov chains (both discrete and continuous), Poisson processes and queues. We will illustrate through different examples the rich diversity of applications of the subject. Topics marked with (*) are optional; a selection of these could be covered depending on the specific interests of the students.

TEXTIntroduction to Probability Models,by Sheldon M. Ross (Academic Press, 8th edition).

COURSE OUTLINE

- Introduction to Stochastic Processes

- Definition
- State space and parameter space
- Examples
- Conditional Probability and Conditional Expectation

- Generalization of conditional probability to random variables
- Computing expectations by conditioning
- Computing probabilities by conditioning
- Discrete Time Markov Chains

- Definition and examples
- Chapman-Kolmogorov equations
- Transience and recurrence
- Stationary distributions
- Sequential decisions and Markov chains (*)
- Simulations and Markov Chain Monte Carlo (*)
- The Poisson Process

- Axiomatic definition
- Waiting time distributions
- Generalizations
- Simulation (*)
- Continuous Time Markov Chains

- Definition
- Birth and death processes
- Transition probabilities; Chapman-Kolmogorov Equations
- Queues

- Definitions and basic structure of a queueing system
- M/M/1, M/M/m, M/G/1 and M/M/m models
- Applications

STUDENT BACKGROUND

Mathematics:This course requires Calculus (MATH 105 or MATH 110), Linear Algebra (MATH 135H) and a strong background in Probability (MATH 155H).## PROBLEM SET POLICY

Problem sets will be posted on MyLearningSystem, with a notification of due date and time. Problem set solutions are to be submitted in class or by the due time in the instructor's drop box on the day they are due. No late submissions are accepted since solutions to assignments will be posted at deadline time.

## MIDTERM EXAMINATION

There will be one midterm examination on Tuesday, October 30.

OTHER IMPORTANT DATESOctober 22-26 is Reading Week. Last day of classes is Friday, December 7.

COURSE EVALUATION

Problem sets: 4 x 10% 40% Midterm exam 1 x 20% 20% Project 1 x 15% 15% Final exam 1 x 25% 25% 100% ## Academic dishonesty:

Academic dishonesty, which includes plagiarism and cheating, is an extremely serious academic offense and carries penalties varying from failure in an assignment to suspension from the University. Definitions, penalties, and procedures for dealing with plagiarism and cheating are set out in Trent University's Academic Dishonesty Policy which is printed in the University Calendar.## Access to instruction:

It is Trent University's intent to create an inclusive learning environment. If a student has a disability and/or health consideration and feels that he/she may need accommodations to succeed in this course, the student should contact the Disability Services Office (BL Suite 109, 748-1281,disabilityservices@trentu.ca) as soon as possible. Complete text can be found under Access to Instruction in the Academic Calendar.