**MATH 275A: Fall 2017**

**Graduate Probability**

lecturer: Marek Biskup, MS 6180

time and place: MWF 10-11 in MS 6201

discussion: R 10-11 in MS 6201

office hours: MWF 1-2

**Final exam:** set for Saturday, Dec 9, 8-11 AM. Location MS 6201 (our regular classroom).

Here are the notes for the last week of lectures covering stable laws and convergence, and infinite divisibility

**Homework assignments: **

HW#1 HW#2 HW#3 HW#4 HW#5 HW#6 HW#7 HW#8

**General information: ** Check out first the course announcement

**Synopsis: **This is the 1st quarter of the 3-quarter graduate probability sequence. A rough plan what should be covered in this quarter is as follows:

- Basic setup of probability theory: measure and integration.
- Infinite product spaces, i.i.d. random variables, Borel-Cantelli lemma, etc.
- Laws of large numbers (weak and strong) for independent random variables.
- Convergence in distribution, central limit theorem.
- Stable laws, infinite divisibility, limit laws for heavy-tailed random variables.
- Conditional expectation and probability.

**Literature & resources: **

Principal textbook: R. Durrett *Probability: Theory and Examples*, Cambrige Univ. Press. (see online version)

Other resources will be distributed as we go on.

**Course credit: **

**Scheduling: **