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):

- Durrett, Probability: Theory and Examples, 5th edition (Ch. 4,6).
- 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:** 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: **

- Durrett: 4.1-4.9,5.1-5.2,6.1-6.5;
- Williams: 6,9--14;
- Billingsley: most of 32--35, 24 and part of 22.

See also seminar for current activity in related areas.