Tuesday, 9:30-11:20, Courant 1302, 3 units. Official course description.

Prerequisites: a first course in probability, familiarity with Lebesgue integral, or G63.2430 Real Variables I as corequisite.

This is the first part of a two-part course, continued by R. Varadhan in the spring. The fall term will cover limit theorems (laws of large numbers, central limit theorem), Markov chains (discrete time), and martingales (Doob's inequality and the martingale convergence theorem).

I recommend that students print out Varadhan's lecture notes , which will serve as our primary textbook.

Problem Set One

Problem Set Two

Problem Set Three

Problem Set Four

Problem Set Five

Problem Set Six

Problem Set Seven

Problem Set Eight

Final Exam