Schedule (subject to change, last updated 9/19/19)

Abbreviations:

• Ç: E. Çinlar, Probabiilty and Stochastics, available as a PDF through the UBC library.
• B: P. Billingsley, Probabiliy and Measure, 3rd ed.
• D: R. Durrett, Probability: Theory and Examples, 5th ed. available as a PDF on the author’s website
• G: A. Gut, Probability: A Graduate Course, available as a PDF through the UBC library.
• G&S: G. Grimmett and D. Stirzaker, Probability and Random Processes, 3rd ed.

Class meeting	Date	Notes	Topics	Readings (required)	Readings (supplemental)	Homework (out)	Homework (due)
1	9/4		Intro & logistics; motivation
2	9/9		Measurable spaces	Ç I.1		Assignment 1
3	9/11		Measurable spaces continued; measurable functions	Ç I.2
4	9/16		Measurable functions continued; measures	Ç I.2-3
5	9/18		Measures continued
6	9/23		Probability spaces; random variables; distributions	Ç II.1, II.4; G 2.2 (skip sec. 2.2.2)	G&S 1.1-1.3; G 1.3; D 1.2; G&S 2*
7	9/25		Integration	Ç I.4	D 1.4-5; B 3.15-17		Assignment 1
-	9/27					Assignment 2
8	9/30		Integration and expectation	Ç I.4, II.2	D 1.6; G 2.5-8; G 4; G&S 5
9	10/2		Expectation; changes of measure; inequalities	Ç I.5, II.2
10	10/7		Transforms; independence	Ç II.2, II.5	G 5, 6; D 2*
11	10/9		Conditional expectation (guest lecturer)	Ç IV.1
-	10/11						Assignment 2
12	10/14	Thanksgiving	No class
13	10/16	MIDTERM	MIDTERM (regular time and location)
14	10/21		Conditional expectations; conditional probability	Ç IV.1-3; Ç I.6	G 2.9; G&S 1.4, 3.7, 4.6; D 1.7; B 3.18	Assignment 3
15	10/23		Conditioning continued; conditional independence	Ç IV.1-3	B 6.33-34
16	10/28		Conditional independence continued; martingales	Ç IV.4
17	10/30		Martingales; convergence	tbd
18	11/4		Martingales; convergence	tbd
19	11/6		Poisson random measures	tbd		Assignment 4	Assignment 3
20	11/11	Remembrance Day	No class
21	11/13		Poisson random measures	tbd
22	11/18		Brownian motion	tbd
23	11/20		Brownian motion	tbd
24	11/25		Markov chains	tbd			Assignment 4
25	11/27		Symmetry and invariance	tbd