18.675. Theory of Probability.
Fall 2019, MW 11:00-12.30 in 4-237.
Sums of independent random variables, central limit phenomena, infinitely divisible laws, Levy processes, Brownian motion, conditioning, and martingales. This is a re-numbering of 18.175, and will be similar to recent versions of the course taught by Vadim Gorin and Scott Sheffield.
Prerequisite: 18.100A, 18.100B, 18.100P, or 18.100Q.
Prior exposure to probability (e.g. 18.600) is strongly recommended.
Instructor: Nike Sun (nsun at ##), office hours Mondays 2-4pm in 2-432.
TAs: Sergei Korotkikh (korotkih at ##), office hours Tuesdays 1-2pm in 2-231D;
and Zhulin Li (zhulin at ##), office hours Fridays 5-6pm in 2-231A.
## = mit dot edu. Please include "18.675" in the subject line of all emails.
Homework will be announced here and posted on Stellar.
TEXTBOOKS. References marked * are available electronically through libraries.mit.edu.
[online] R. Durett, Probability: Theory and Examples, Cambridge UP, 2019.
[online] *O. Kallenberg, Foundations of Modern Probability. Springer, 1997.
LECTURE NOTES. These notes were compiled for similar classes.
A. Dembo, Stanford Math 230 / Stat 310 (most detailed notes available that I know of).
D. Aldous, Berkeley Math 218A / Stat 205A, notes compiled by Sinho Chewi.
Homework (25%), exam 1 (35%), exam 2 (35%), class participation (5%). No makeup exams will be given for any scheduling conflict, including other classes. See the course syllabus (on Stellar) for the full grading policy.
SCHEDULE OF TOPICS. I will keep this document up to date with a list of main topics covered.
Andrew Lin has kindly agreed to share his class notes, with the disclaimer that these are not checked by the course instructors.
Key dates: exam 1 Monday October 21, exam 2 Wednesday December 4.
ANNOUNCEMENTS. All assignments and solutions are on Stellar.