The second quarter in a yearly sequence of probability theory. Main topics are stopping times, random walks, conditional expectation, discrete time martingales, exchangeability, renewal theory and applications to Markov chains of countable state space.
The spring quarter (Stat310C) is to concentrate on continuous time martingales, infinitely divisible laws, Brownian motion and introduction to stochastic calculus.
Prerequisites: Students should be comfortable with integration and measure theory and should have mastered the material of a graduate probability course covering Laws of Large Numbers, Weak Convergence and Central Limit Theorems. Specifically, you may take this class for credit if you had at least grade B in Stat310A/Math230A. Otherwise, you'll need instructor's permission for doing so.
Text: Lecture notes of STAT310b (Mar. 31 version). See also STAT310a lecture notes (Feb. 28 version) .
Supplementary texts (on reserve at math. library):
Meeting: Sequoia 200, MWF 1:15 - 2:05.
Instructor: Amir Dembo, Office hours M, W 11:00-12:00 or e-mail
TA1 (grading HW1, HW3, HW5, HW7, HW9): Guillaume Horel, Sequoia 231, office hours W 2:10-3:10 Th 1:00-2:00. or e-mail
TA2 (grading HW2, HW4, HW6, HW8): Kshitij Khare, Sequoia 237, office hours Tu 1:00-3:00. or e-mail
Grading : Judgement based on final exam mark (70%) and on consistent Homework efforts (30%).
Final : Thursday 3/22, 8:00am-12:00pm (four hours), Sequoia 200, open material. See checklist for material. See 2007 final and its solution .
Homework: Five homework problems from lecture notes, due Friday 1:15 p.m. on a weekly basis, starting January 19th. See all Homework sets including rules and weekly reading assignments and the solution of HW sets. Please deliver your assignment to the course mailbox (marked "STAT 310b") in Sequoia the day it is due (course mailbox is in 2nd floor of the building). Late homework will not be accepted. Your assignment will typically be graded by the following Friday and placed in the course mailbox. Graded HW9 returned on March 20th! Solutions are posted on this page within 48h of the due date.
Syllabus (per lecture notes):
1/8 M(--) W(4.1) F(4.2) 1/15 M(--) W(4.3) F(4.4) 1/22 M(5.1.1) W(5.1.2) F(5.4) 1/29 M(5.3) W(5.3.1) F(5.2.2/5.3.2) 2/5 M(5.2) W(5.5.1) F(5.5.2) 2/12 M(5.5.2/5.5.3) W(5.5.3) F(6.1) 2/19 M(--) W(6.1) F(6.2) 2/26 M(6.3) W(6.3/6.4) F(6.4) 3/5 M(6.4/6.5) W(6.5) F(6.5) 3/12 M(6.5) W(6.5/Review) F(Q&A)
Material covered, including HWs and self-reading:
See also seminar for current activity in related areas.