Theory of Probability (MATH230C/STAT310C, Spring 2017)

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:

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:

See also seminar for current activity in related areas.