This probability theory course covers products measures and sums of independent variables, convergence of laws and central limit theorems, conditional expectations and martingales. I hope to also touch upon ergodic theory and continuous time stochastic processes.

Intended for students familiar with measure theory (possibly of no exposure to probability theory), this course provides the prerequisite for advanced stochastic processes courses such as Math234/236/237 or Stat310c/317/318.

Students should solve correctly half of the problems in the four homework sets (HW1 due 4/21, HW2 due 5/5, HW3 due 5/19, HW4 due 6/2 on class, typically graded within a week).

Text, any of the following:

- Dudley, Real Analysis and Probability (Ch. 8-10 and part of 12).
- Stroock, Probability Theory: An analytic view (Ch. 1-2 and parts of 3 and 5).
- Durrett, Probability theory and Examples. 2nd Ed. (Ch. 1,2,4 and parts of 6,7).

** Prerequisite: ** Mathematics 205a/b or
familiarity with measure theory, (Lesbegue) integration and
basic elements of real/functional analysis.

** Meeting:** Math. 380F MWF 10:00 - 11:00.

** Instructor: **
Amir Dembo,
Math. 382H WF 11:00-12:00, or e-mail
amir@math.stanford.edu

See also seminar for current activity in related areas.