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 provide an introduction to continuous time stochastic proceses. Specifically, it typically covers continuity and modification, Gaussian and Markov processes, continuous time martingales, Brownian motion and it properties, invariance principles with applications to CLT and LIL, infinitely divisible laws and jump processes.
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.
Posted text: Chapters 4-6 of STAT310/MATH230 lecture notes. With future updated changes if needed.
Supplementary texts (on reserve at math. library):
Meeting: Sequoia 200, M W 9:30 - 10:45.
Instructor: Amir Dembo, Office hours, Sequoia 129, W 4:10-5:30PM; or e-mail .
TA1 (grading HW1, HW3, HW5, HW7, HW9/Final): Anirban Basak, Office hours, Sequoia 208, Tu 3:00-6:00PM; or e-mail
TA2 (grading HW2, HW4, HW6, HW8, HW9/Final): Ruojun Huang. Office hours, Sequoia 211, M 11:30-1:30, Tu 1:00-2:00PM; or e-mail
Grading : Judgement based on final exam mark (70%) and on consistent Homework efforts (30%). Typically, total score above 63% needed for passing.
Final exam : Wednesday 3/20, 8:00am-12:00pm (note extra time), Sequoia 200, open material; Material: Chapters 4-6 of lecture notes. Final exam and its solution Posted 1PM, April 1.
Homework: Solve four of five homework problems from lecture notes, due Wednesday 11:00 a.m. on a weekly basis. See HW1-HW9 (with practice problems) and solutions of SOL HW1, SOL HW2, SOL HW3, SOL HW4, SOL HW5, SOL HW6, SOL HW7, SOL HW8, SOL HW9, SOL practice problems. 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 Wednesday and placed in the course mailbox. Solutions are posted on this page within 24h-72h of due date.
Syllabus (per lecture notes):
1/7 M(4.1;4.2) W(4.2;4.3) 1/14 M(4.4) W(---) 1/21 M(---) W(5.1) 1/28 M(5.4;5.3) W(5.2.2;5.3;5.3.1) 2/4 M(5.2;5.3.2) W(5.3.2;5.5.1) 2/11 M(5.5.2) W(5.5.3) 2/18 M(---) W(6.1) 2/25 M(6.2/6.2.1) W(6.2.1/6.2.2) 3/4 M(6.2.2/6.2.3) W(6.2.3/6.3.1) 3/11 M(6.3.1) W(6.3.2) F(Review)
Material covered, including HWs and self-reading:
See also seminar for current activity in related areas.