Class number 054–39482R
Class meetings: MW, 9:30am-12:30pm, KAP 163.
Information on this and related pages changes frequently.
Instructor: Sergey Lototsky.
Office: KAP 248D.
Phone: 213 740 2389
E-mail: lototsky usc edu.
Office Hours: MW after the class. Appointments at other time are welcome.
Course objective: to get used to mathematical tools for quantifying and modeling extreme and/or unlikely behavior.
More general goal: to learn something interesting, new, and/or useful.
Official grading scheme: 20% class participation, 40% homework assignments, 40% final presentation.
Main reference: Sidney I. Resnick. Extreme values, regular variation and point processes. Reprint of the 1987 original. Springer Series in Operations Research and Financial Engineering, Springer, New York, 2008. xiv+320 pp. ISBN: 978-0-387-75952-4
This book is indeed three-in-one: Regular Variation Point Processes
An example of a book review from Math reviews [Edition 1, Edition 2] and from the Bulletin of the AMS
My notes
- Basic inequalities
- Gaussian objects: Normal random variables, CLT, and more
- A summary of Brownian motion
- Lambert’s W function
- Gamma and Beta Functions
- Cauchy’s functional equation
- Cauchy distribution
- About harmonic numbers
- Weak convergence of probability measures
- LDP and rare events
- Extremes
- A summary of large deviations
- A summary of the Cameron-Martin-Girsanov theorem and related results
Other notes
- (Almost) everything you need to know about probability distributions
- Coupon collection problem (an example where an extreme value distribution can appear in the limit)
- Determinant point processes
- All about Cauchy’s functional equation
- Lambert’s W function
Our progress.
May 15. An overview of the class, the book, and some foundational material from real analysis and probability; three types of extreme value distributions.
Related material: Convergence of random variables and an illustration
May 20.
May 22.
May 27. No class (Memorial Day, University Holiday)
May 29.
June 3.
June 5.
June 10.
June 12.
June 17.
June 19. No class (Juneteenth, Non-Instructional Day)
June 24.
June 26.
July 1.