Theory of Probability (MATH230B/STAT310B, Winter 2015)

The second quarter in a yearly sequence of probability theory. Main topics are stopping times, random walks, conditional expectation, discrete time martingales, Markov chains, exchangeability, renewal and ergodic theory.

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 (up to the start of 6.2.1), from STAT310/MATH230 lecture notes. See also additions and updates (as of Mar. 17), and scribe notes: ergodic theory.

Supplementary texts:

Meeting: Sequoia 200, M W 9:30-10:45AM.

Instructor: Amir Dembo, Office hours, Sequoia 129, W 12:00-1:00PM; or e-mail .

TA1 (grading HW1, HW3, HW5, HW7, HW9/Final): Snigdha Panigrahi, Office hours, Sequoia 105, M 2:00-4:00PM, Sequoia 241, Tu 11:00AM-12:00; Up to March 13! or e-mail

TA2 (grading HW2, HW4, HW6, HW8, HW9/Final): Jessica Hwang, Office hours, Sequoia 241, Tu 1:00-4:00PM; 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 (solution): Wednesday 3/18, 8:00am-12:00pm, Sequoia 200, open material; Material: Chapters 4-6.2 of lecture notes and Durrett Chapter 7.

Homework: Solve four of five homework problems from lecture notes, due Wednesday 10:45 a.m. on a weekly basis. See HW1-HW7(+exam practice problems), HW8-HW9 and SOL1, SOL2, SOL3, SOL4, SOL5, SOL6, SOL7, SOL8+SOL9, SOL:practice problems. Please deliver your assignment to class the day it is due Late homework will not be accepted. Your assignment will typically be graded and returned in class the following week (HW9: collect from STAT310b mail-box in Sequoia, 2nd floor). Solutions are posted on this page within 24h-72h of due date.

Syllabus (per lecture notes; D=Durrett):

	1/5     M(4.1.1;4.2)       W(4.2;4.3)          
	1/12    M(4.4;4.1.2)       W(5.1)          
	1/19    M(---)             W(5.1;5.4)  
	1/26    M(5.2.2;5.3;5.3.1) W(5.2;5.3.1;5.3.2)       
	2/2     M(5.3.2;5.5.1)     W(5.5.1;5.5.2)   
	2/9     M(5.5.2;5.5.3)     W(5.5.3;6.1)
	2/16    M(---)             W(6.1)        
	2/23    M(6.1;6.2)         W(D=7.2;7.1)
	3/2     M(D=7.2;7.1)       W(D=7.3)      
	3/9     M(D=7.5;7.4)       W(Review)

Material covered, including HWs and self-reading:

See also seminar for current activity in related areas.