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; A list of updates is to be posted when relevant .
Supplementary texts (on reserve at math. library):
Meeting: Sequoia Hall 200, Tu/Th 9:25-10:50 a.m (+10 min added to compensate for 2 lectures canceled).
Instructor: Amir Dembo, Office hours, Sequoia 129; Th 12:15-1:30 p.m. or e-mail
TA1 (grading HW2, HW4, HW6, HW8, HW9): Zhen Zhu, Office hours, Sequoia 231; M 4:00-6:00 p.m. No Friday office hours or e-mail .
TA2 (grading HW1, HW3, HW5, HW7, HW8): Nike Sun, Office hours, Sequoia 242; M 1:10-2:10 p.m., Tu 11:00-1:00 p.m. 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 and solution:: Wednesday, June 13, 12:15-4:15 p.m. Note: 4h exam! Sequoia 200; Bring only lecture notes and HW solutions; Material: Chapters 7-9 of lecture notes. See also practice final exam, with solution for practice exam as well as list of key-items.
Homework: Four HW problems out of the five assigned are due Tu 3:00 p.m. on a weekly basis. See homework sets, HW1-HW9 (revised reading to match schedule changes) and the solutions of HW1-HW5 (HW5 posted 5/13/). Please deliver your assignment either to the TA office hours 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 and returned to class or the course mailbox (marked "STAT 310c Out") in Sequoia within a week of due date.
Syllabus (per lecture notes):
4/3 Tu(7.1/7.2) Th(7.2/7.3)
4/10 Tu(8.1) Th(8.2.1/8.2.2)
4/17 Tu(8.2.2) Th(8.2.3/8.3.1)
4/24 Th(8.3.1) Th(8.3.2)
5/1 Tu(---) Th(TA: Q/A)
5/8 Tu(9.1) Th(9.1/9.2)
5/15 Th(9.2) Th(9.2.1/9.2.2)
5/22 Tu(9.2.2/9.3) Th(8.2.4)
5/29 Tu(8.2.4) Th(8.3.3)
6/5 Tu(8.3.3) Th(Opt: Review)
Material covered, including HWs and self-reading:
See also seminar for current activity in related areas.