Math 285, Stochastic Processes, Spring 2017
Course Content
Stochastic processes have a wide range of applications throughout the biological, computational, and physical sciences. This course provides an introduction to stochastic processes at the beginning graduate level. Topics covered will include Markov Chains in discrete and continuous time, martingales, and Brownian motion. The prerequisites for the course are calculus, linear algebra, and undergraduate probability at the level of Math 180A. The course will focus on the theory of stochastic processes rather than specific applications, but technical details will be kept to a minimum so that the course is accessible to a wide audience.
Textbook
There is no required textbook for the course. Useful references are Markov Chains by James Norris and Introduction to Stochastic Processes by Greg Lawler. Norris' book is available online through the UC San Diego library web site here, provided you are connecting from on campus.
Who should take this course?
This course is designed primarily for graduate students in departments other than Mathematics who would like to learn more about stochastic processes. The course should also be at the right level for Masters students in Mathematics or Statistics who would like to learn about stochastic processes but do not have the more extensive background in real analysis that is required for Math 280ABC. Ph.D. students in Mathematics who either do not have time to take the full Math 280ABC sequence or who would like to develop their intuition about stochastic processes before taking Math 280ABC could also consider Math 285. Students interested in doing research in the theory of probability or stochastic processes, however, will need take Math 280ABC and probably also Math 286. Undergraduates are encouraged, if possible, to take Math 180B and Math 180C instead of Math 285.