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,
enrollment is capped and graduate students may register for
credit only if they have earned at least a
grade A- in Stat310A/Math230A. All other students should email to
secure the instructor's permission for doing so
(in particular, this applies to all undergraduate/co-term students).

Text: Chapters 4-7 (Chapter 6 only to start of 6.2.1), from STAT310/MATH230 (See also list of changes).

Supplementary texts (most are available online via Stanford):

- 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:** Tu Th 8:30-9:55am (PST). Synchronous,
recorded (Panopto edited), white-board (Zoom) lectures, with breakout rooms and
TA monitoring of chat-line.

Pre-teaching (non-recorded) Zoom meeting: Th 8:30-9:20am, 1/7 (PST), for informal chat and community building.

** Instructor: **
Amir Dembo,
Office hours: Tu 9:55-10:20am, Th 9:55-10:20am
(non-recorded, public continuation of lecture Zoom meetings).
Use ** Piazza ** or TA office hours for all questions (especially on HWs),
or e-mail Amir
(with MATH230B/STAT310B as your email subject), if a (confidential)
private meeting needed (during the term expect reply within 24h).

** TA1 (grading HW1, HW3, HW5, HW7, HW9; chat at lectures)**:
Chenyang Zhong. Office hours:
Th 11:00-12:30pm **(up to 3/15),** or e-mail
Chenyang
(with MATH230B/STAT310B as your email subject).

** TA2 (grading HW2, HW4, HW6, HW8, HW9)**:
Yuchen Wu. Office hours:
** Tu 5:45-7:15pm, ** We 5:30-7:00pm, Fr 11:00-12:30pm **(up to 3/15)**
or e-mail Yuchen
(with MATH230B/STAT310B as your email subject).

** Grading **: Judgement based on final exam mark (64%),
and on consistent Homework (30%) and participation (6%) efforts
(details in recording posted on Panopto within Canvas).
Typically, total score above 63% needed for passing.
Any dispensation for adverse health/housing mandates
be contingent on its applicability also
for Math. and Stat. PhD-s.

** Final Exam: ** Open books. A ** 4h timed ** exam
taken by Gradescop within a ** 24h time frame, starting
5:00am PST, Mon 3/15 ** (hence upload end-of-frame be 5:00am PST, Tue 3/16).

** Material: ** Chapters 4-6.2 (up to 6.2.1), and Sections 7.1-7.3
of lecture notes.

** Study tools: **
Practice-Exercises **(+solutions posted on Canvas)**
and Practice Final ** (Posted on Canvsas) ** with solution
via ** Gradescope, Fri 3/12.**

** Homework: ** On a weekly basis, solve four of five homework problems
from lecture notes, as ** posted ** at
HW1-HW9.
** (+Final Practice Exercises ** on 2nd page).
Problems are due each **Saturday 8:00am.**
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 33h of due date.

** Syllabus ** (per lecture notes):

1/4 Tu(---) Th(Informal) 1/11 Tu(4.1.1;4.2) Th(4.2;4.3) 1/18 Tu(4.4;4.1.2) Th(5.1) 1/25 Tu(5.1;5.4) Th(5.2.2;5.3;5.3.1) 2/1 Tu(5.2;5.3.1) Th(5.3.2) 2/8 Tu(5.5.1;5.5.2) Th(5.5.2) 2/15 Tu(5.5.3) Th(6.1) 2/22 Tu(6.1) Th(6.1;6.2;7.1) 3/1 Tu(7.1;7.2) Th(7.2) 3/8 Tu(7.2;7.3) Th(Review) 3/15 Tu(7.4) Th(Topics:6.2-6.3)

** 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.