Lectures: MWF 2-3, 66-168

Office hours: Monday 3-4 and Wednesday 3-4 in E17-312.

Assignments: 7 term problem sets (worth 10% of grade) and 1 final problem set (worth 30% of grade).

Official course description: Sums of independent random variables, central limit phenomena, infinitely divisible laws, Levy processes, Brownian motion, conditioning, and martingales.

Texts: There are many excellent textbooks and sets of lecture notes that cover the material of this course, several written by people right here at MIT. The course material is contained in the union of the following online texts for first-year graduate probability courses:

- S.R.S. Varadhan's lecture notes
- Amir Dembo's lecture notes
- Rick Durrett's book at CiteSeer or at Amazon and here is a recently updated version from Durrett's web page
- Noel Vaillant's www.probability.net tutorials
- Dmitry Panchenko's notes for an earlier rendition of 18.175 .

TENTATIVE SCHEDULE

- Lecture 1 (February 5): Probability spaces and sigma-algebras
- Lecture 2 (February 7): Extension theorems: a tool for constructing measures
- Lecture 3 (February 10): Random variables and distributions
- Lecture 4 (February 12): Integration
- Lecture 5 (February 14): More integration and expectation
- Lecture 6 (February 18): Laws of large numbers and independence
- Lecture 7 (February 19): Sums of random variables
- Lecture 8 (February 21): Weak laws and moment-generating and characteristic functions
- Lecture 9 (February 24): Borel-Cantelli and the strong law of large numbers PROBLEM SET DUE
- Lecture 10 (February 26): Zero-one laws and maximal inequalities
- Lecture 11 (February 28): Independent sums and large deviations
- Lecture 12 (March 3): DeMoivre-Laplace and weak convergence
- Lecture 13 (March 5): Large deviations PROBLEM SET DUE
- Lecture 14 (March 7): Weak convergence and characteristic functions
- Lecture 15 (March 10): Characteristic functions and central limit theorem
- Lecture 16 (March 12): Central limit theorem variants
- Lecture 17 (March 14): Poisson random variables PROBLEM SET DUE
- Lecture 18 (March 17): Stable random variables
- Lecture 19 (March 19): Higher dimensional limit theorems
- Lecture 20 (March 21): Infinite divisibility and Levy processes
- Lecture 21 (March 31): PROBLEM SET DUE
- Lecture 22 (April 2):
- Lecture 23 (April 4): Random walks
- Lecture 24 (April 7):
- Lecture 25 (April 9): Reflections and martingales
- Lecture 26 (April 11): More on martingales PROBLEM SET DUE
- Lecture 27 (April 14): More on martingales
- Lecture 28 (April 16): Even more on martingales
- Lecture 29 (April 18): Still more martingales
- Lecture 30 (April 23): Markov chains, PROBLEM SET DUE
- Lecture 31 (April 25): More Markov chains
- Lecture 32 (April 28): Additional material on Markov chains
- Lecture 33 (April 30): Ergodic theory
- Lecture 34 (May 2): More ergodic theory PROBLEM SET DUE
- Lecture 35 (May 5): Ergodic theory
- Lecture 36 (May 7): Brownian motion
- Lecture 37 (May 9): More Brownian motion
- Lecture 38 (May 12): Even more Brownian motion
- Lecture 39 (May 14): Last lecture FINAL PROBLEM SET DUE