Theory of Probability (MATH230B/STAT310B, Winter 2020)

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 processes. 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 (this in particular applies for all undergraduate students).

Text: Chapters 4-7.3 (Chapter 6 only to start of 6.2.1), from STAT310/MATH230 (ignore 7.4, preliminary draft). See also Changes.

Supplementary texts (on reserve at the science library):

Meeting: Gates B12, Tu Th 9:00-10:20AM.

Instructor: Amir Dembo, Office hours (to 3/8), Sequoia 129, Tu 4:30-5:30pm, or e-mail e-mail (please include MATH230B/STAT310B in email subject).

TA1 (grading HW1, HW3, HW5, Final): Sky Cao, Office hours (to 3/8), Sequoia 207, We 4:30-6:00pm, Th 5:45-7:15pm, or e-mail e-mail (please include MATH230B/STAT310B in email subject).

TA2 (grading HW2, HW4, HW6, HW7, HW8, HW9): Fang Cai, Office hours (to 3/8), 120-414 on Th 1:30pm-3:00pm; Sequoia 207 on Fr 10:00am-11:30pm, or e-mail e-mail (please include MATH230B/STAT310B in email subject).

Grading : Judgement based on final exam mark (70%) and on consistent Homework efforts (30%). Typically, total score above 63% needed for passing.

Download FinalCanceled! Upload on Gradescope within +10 min of end of exam.

Material: Open books; Material: Chapters 4-6.2 and Chapter 7.1-7.3 of lecture notes.

Study tools: Practice-Exercises (with solution on Canvas), and Practice Final (with solution on Canvas).

Homework: Solve four of five homework problems from lecture notes, due Friday 2:30pm on a weekly basis. See HW1-HW9. Assignments will be submitted through Gradescope by the due date/time. Late homework will not be accepted. Your assignment will typically be graded and returned on Gradescope the following week. Solutions are posted (on the course Canvas page), within 24h-72h of due date.

Syllabus (per lecture notes):

	1/6     Tu(4.1.1;4.2)        Th(4.2;4.3)          
	1/13    Tu(4.4;4.1.2)        Th(5.1)          
	1/20    Tu(5.1;5.4)          Th(5.2.2;5.3;5.3.1)
	1/27    Tu(5.2;5.3.1)        Th(5.3.2)     
	2/3     Tu(5.5.1;5.5.2)      Th(5.5.2)
	2/10    Tu(5.5.3)            Th(6.1)     
	2/17    Tu(6.1)              Th(6.1;6.2)
        2/24    Tu(7.1)              Th(7.2)
	3/2     Tu(7.2;7.3)          Th(7.3)
        3/9     Tu(---)              Th(---)

Material covered, including HWs and self-reading:

See also seminar for current activity in related areas.