Math 357H: Introduction to Stochastic Processes

Fall 2007

COURSE  TOPICS

The 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.

TEXT

COURSE OUTLINE

1. Introduction to Stochastic Processes
   1. Definition
   2. State space and parameter space
   3. Examples
2. Conditional Probability and Conditional Expectation
   1. Generalization of conditional probability to random variables
   2. Computing expectations by conditioning
   3. Computing probabilities by conditioning
3. Discrete Time Markov Chains
   1. Definition and examples
   2. Chapman-Kolmogorov equations
   3. Transience and recurrence
   4. Stationary distributions
   5. Sequential decisions and Markov chains (*)
   6. Simulations and Markov Chain Monte Carlo (*)
4. The Poisson Process
   1. Axiomatic definition
   2. Waiting time distributions
   3. Generalizations
   4. Simulation (*)
5. Continuous Time Markov Chains
   1. Definition
   2. Birth and death processes
   3. Transition probabilities; Chapman-Kolmogorov Equations
6. Queues
   1. Definitions and basic structure of a queueing system
   2. M/M/1, M/M/m, M/G/1 and M/M/m models
   3. 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 DATES

October 22-26 is Reading Week.   Last day of classes is Friday, December 7.

COURSE EVALUATION

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.