The third quarter in a yearly sequence of probability theory serves as an introduction to the theory of continuous time stochastic proceses. Covering continuity and modification, Gaussian and Markov processes, continuous time martingales, Brownian motion and its properties, invariance principles with applications to CLT and LIL.

** Prerequisites: ** Students should have mastered a graduate
probability course covering conditional expectation, discrete time
martingales and Markov chains. Specifically,
you may take this class for credit if you had at least grade B in
Stat310B/Math230B. Otherwise, you'll need instructor's
permission for doing so.

** Posted lecture notes: **
Chapters 7-9 of
STAT310 notes; See also list of
updates up-to 6/5.

Supplementary texts:

- Durrett, Probability: Theory and Examples, 4th edition (Ch. 8).
- Karatzas and Shreve, Brownian Motion and Stochastic Calculus, 2nd edition (Ch. 1-2).
- Billingsley, Probability and Measure, 3rd edition (Ch. 7).
- Dudley, Real Analysis and Probability (Ch. 12).
- Breiman, Probability (Ch. 12--15).
- Morters and Peres, Brownian motion (Ch. 1,2,5).
- Kallenberg, Foundations of Modern Probability (Ch. 12--14 and part of Ch. 17--19).

** Meeting:** 380-380F, Tu/Th, 9:00-10:20 a.m.

** Instructor: **
Amir Dembo,
Office hours: Th 10:30-11:30 a.m. at Sequoia 129
or e-mail

** TA1 (grading HW1, HW3, HW5, HW7, HW9): **
Jun Yan, Office hours: M 12:20-1:20 p.m. at Sequoia 105;
F 2:00-4:00 p.m. at 380-381U; or
e-mail .

** TA2 (grading HW2, HW4, HW6, HW8, HW9): **
Ruojun Huang, Office hours: M 5:30-6:30 p.m., W 4:00-6:00 p.m.
both at Sequoia 105,
or e-mail .

** Grading **: Judgement based on final exam mark (73%)
and on consistent Homework efforts (27%).
Typically, total score above 63% needed for passing.

** Final exam
(solution):**
Monday, June 12, 8:00-12:00 p.m. 380-380Y;
Bring only lecture notes and HW solutions;
Material: Chapters 7-9 of lecture notes.
To prepare, see
practice final , with
solution,
and
list of key-items.

** Homework: ** Four HW problems out of the five assigned
are due Tu 4:00 p.m. on a weekly basis.
See
homework sets
and their
solution.
Please deliver your assignment either to the lecture
or to the course mailbox (marked "STAT 310c In") in
Sequoia, the day it is due (course mailbox is in 2nd floor of
the building). Late homework will not be accepted.
Solutions are posted on this page (within 36h).
All unclaimed solutions are in mailbox marked "STAT 310c Out".

** Syllabus ** (per lecture notes):

4/4 Tu(7.1) Th(7.2) 4/11 Tu(7.3/8.1) Th(8.1/8.2.1) 4/18 Tu(8.2.2) Th(8.2.2/8.2.3) 4/25 Th(8.3.1) Th(8.3.1/8.3.2) 5/2 Tu(8.3.2/9.1) Th(9.1/9.2) 5/9 Tu(9.2) Th(9.2.1) 5/16 Th(9.2.1/9.2.2) Th(9.2.2/9.3) 5/23 Tu(9.3/8.2.4) Th(8.2.4) 5/30 Tu(8.3.3) Th(8.3.3) 6/6 Tu(Review)

** Material covered, including HWs and self-reading: **

- Durrett: Ch. 8 and Karatzas and Shreve 1-2; Supplements from Breiman 12-15, Billingsley 36-38 and Dudley 12.

See also seminar for current activity in related areas.