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:

- Durrett, Probability: Theory and Examples, 4th edition (Ch. 5,7).
- Williams, Probability with Martingales (Ch. 9 -- 15).
- Billingsley, Probability and Measure, 3rd edition (Mostly 24,31--35).
- Dudley, Real Analysis and Probability (Ch. 10).

** 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: **

- Durrett: 5.1-5.7,6.1-6.3,7.1-7.5;
- Williams: 6,9--14;
- Billingsley: most of 32--35, 24 and part of 22.

See also seminar for current activity in related areas.