Fall 2016
Meetings: TR 1PM2:15PM, Van Vleck B115 Social Sciences 6203
Instructor: Benedek Valkó
Office: 409 Van Vleck
Phone: 2632782
Email: valko at math dot wisc dot edu
Office hours: W 2:30PM3:30PM or by appointment
I will use the class email list to send out
corrections, announcements, please check your wisc.edu email
from time to time.
If you try to register, you may find the class full. In that case sign up for the waitlist. Waitlisted students will typically find a place in the course eventually, and you may also attend lectures in the meantime (assuming there is space in the classroom).
Measure theory is a basic tool for this course. A suitable background can be obtained from Math 629 or Math 721. Chapter 1 in Durrett covers the measure theory needed. We will very briefly review some measure theory at the beginning of the semester. Prior exposure to elementary probability theory could be useful.
Foundations, properties of probability spaces 
Independence, 01 laws, strong law of large numbers 
Characteristic functions, weak convergence and the central limit theorem 
Conditional expectations 
Martingales 
Course grades will be based on biweekly home work assignments
(30%), a midterm exam (30%) and the final exam (40%). We will have
an evening midterm exam on Wednesday, November 2,
7:15pm8:45pm in room B239 Van Vleck. In exchange, the
class on Thursday, November 3 will be canceled.
Final exam: Thursday, December 15, 5:30pm7:30pm, B239 Van
Vleck.
Piazza
We will be using Piazza for class
discussion. The system is catered to getting you help fast
and efficiently from classmates and myself. Rather than
emailing all questions to me, I encourage you to post your
questions on Piazza. If you have any problems or feedback for the
developers, email team@piazza.com.
Find our class Piazza page at: https://piazza.com/wisc/fall2016/math733_001_fa16/home.
Covered
topics 
Suggested
reading for next week 

Week
1. 9/6, 9/8 
Definition of probability
space, random variables, distribution Sections 1.11.5 
Sections
1.51.7, 2.1 
Week
2. 9/13, 9/15 
Expectation
(inequalities, limits), product measures, independence Sections 1.51.7, 2.1 
Sections 2.12.3 
Week
3. 9/20, 9/22 
Kolmogorov extension
theorem, various types of convergences, Weak law of large numbers (Sections 2.12.4) 
Sections 2.32.5 
Week
4. 9/27, 9/29 
BorelCantelli Lemmas,
Strong Law of Large Numbers, 
Sections
2.5, 3.13.2 
Week
5. 10/4, 10/6 
GlivenkoCantelli Theorem,
Kolmogorov 01 Law Central Limit Theorem for coin flips, Convergence in distribution 
Sections
3.23.3 
Week
6. 10/11, 10/13 
Convergence in
distribution, characteristic functions 
Sections 3.23.4 
Week
7. 10/18, 10/20 
Characteristic functions,
general CLT, examples 
Section
3.63.8 
Week
8. 10/25, 10/27 
LindebergFeller theorem,
Moment problem, Local CLT, 

Week
9. 11/1 
Poisson approximation, coupling midterm exam 

Week
10. 11/8, 11/10 
Poisson processm
Infinitely divisible and stable distributions, convergence in distribution in R^d, multivariate CLT, quick intro to Brownian motion, Conditional expectation 
Section
5.15.2 
Week
11. 11/15, 11/17 
Properties of conditional
expectation, martingales 

Week
12. 11/22 

Week
13. 11/29, 12/1 

Week
14. 12/6, 12/8 

Week
15. 12/13, 12/15 