Math 735 Stochastic Analysis

Fall 2014

Meetings: MWF 9:55-10:45 Van Vleck B119
Instructor: Timo Seppäläinen
Office: Van Vleck 425. Office Hours: MW after class, other times by appointment.
Phone: 263-3624
E-mail: seppalai math wisc edu

Course description

Stochastic analysis is a term that refers to stochastic integration and stochastic differential equations and related themes. Here is a list of topics we expect to cover. The amount of time devoted to the fundamentals in the beginning will depend on the level of background that the audience possesses.
  1. Foundations of probability theory, especially conditional expectation
  2. Generalities about stochastic processes, Brownian motion, Poisson process
  3. Martingales
  4. Stochastic integral with respect to Brownian motion (quick overview of the Math 635 stochastic integral)
  5. Predictable processes and stochastic integral with respect to cadlag martingales and semimartingales
  6. Itô's formula
  7. Stochastic differential equations
  8. Local time for Brownian motion, Girsanov's theorem
  9. White noise integrals and a stochastic partial differential equation


This course has flexible prerequisites. The ideal background would be one or two semesters of graduate measure-theoretic probability theory, such as our 733 or 733-734. An essential prerequisite is a certain degree of mathematical maturity, so familiarity with advanced probability is not absolutely necessary. The course will rely on modern integration theory (measure theory covered in Math 629 and 721) and advanced probability, and we can cover some of these points quickly in the beginning.


Course grades will be based on take-home work and a possible in-class exam. Homework will be posted on Learn@UW. You can also see your score record on Learn@UW.

Lecture notes

The course is based on lecture notes written by the instructor, available on Learn@UW. No textbook purchase is required.

Realized schedule for Fall 2014.

Other material

Instructions for homework

Check out the probability seminar for talks on topics that might interest you.