Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 135B: Stochastic Processes
Approved: 2006-05-01 (revised 2013-01-01, B. Morris)

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Probability and Random Processes, 3rd Edition by Geoffrey R. Grimmett and David R. Stirzaker; Oxford University Press; ISBN-13 # 978-0198572220; $34.00-67.00 via Amazon Books. or Introduction to Probability Models, 8thEdition by Sheldon M. Ross;

Prerequisites:

Completion of course MAT 135A and MAT 22A or MAT 67.

Suggested Schedule:

Lecture(s)

Sections

Comments/Topics

1-2 weeks


Conditional probabilities, expectations and distributions, computing probabilities and expectations by conditioning

1 week


Generating functions and their applications. Branching processes.

2-3 weeks


Discrete time Markov chains. Classification of states, limit theorems, reversibility, chains with finitely many states.

1-2 weeks


Poisson process and continuous time Markov chains.

Additional Notes:

The two suggested books have different advantages and disadvantages; the choice of text may depend on the instructor. Other remaining topics to be chosen include: Martingales; Renewal Theory; Random walks; and Brownian motion.

Learning Goals:

This is a second course in probability. The focus is on random processes that evolve over time. Upon completing the course, students will know how to compute limits of random variables. They will know how to compute the moment generating function of a random variable and find large-deviation bounds for sums of independent random variables. They will know how to find the stationary distribution of Markov chain and find the extinction probability of a branching process.

Assessment:

The grade is decided by homework, quizzes, midterms and a final exam.