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: 20060501 (revised 20130101, 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; ISBN13 # 9780198572220; $34.0067.00 via Amazon Books. or Introduction to Probability Models, 8thEdition by Sheldon M. Ross;
Prerequisites:
MAT 135A; (MAT 022A or MAT 027A or MAT 067 or BIS 027A).
Suggested Schedule:
Lecture(s) 
Sections 
Comments/Topics 
12 weeks 
Conditional probabilities, expectations and distributions, computing probabilities and expectations by conditioning 

1 week 
Generating functions and their applications. Branching processes. 

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

12 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 largedeviation 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.
AS A CAPSTONE:
Students will develop and deepen their understanding of stochastic
processes in this second course of the MAT 135 sequence. While learning
about random processes that evolve over time, they will gain mastery of
this specialization and improve their ability to communicate mathematics at
the capstone level, commensurate with that expected of one with an
undergraduate degree in mathematics.
Assessment:
The grade is decided by homework, quizzes, midterms and a final exam.