AMS 569: Probability Theory
This page is part of my personal academic record, not an official course website.
Course description
Probability spaces and sigma-algebras. Random variables as measurable mappings. Borel-Cantelli lemmas. Expectation using simple functions. Monotone and dominated convergence theorems. Inequalities. Stochastic convergence. Characteristic functions. Laws of large numbers and the central limit theorem.
Textbooks and resources
Required textbook
- Probability Essentials by Jean Jacod and Philip Protter, 2nd edition, 2004, Springer
Supplementary textbooks
- A Probability Path by Sidney I. Resnick, 2005, Birkhäuser
- Probability: Theory and Examples by Rick Durrett, 5th edition, 2019, Cambridge University Press
- Probability and Measure by Patrick Billingsley, 3rd edition, 1995, Wiley
- A Course in Probability Theory by Kai Lai Chung, 3rd edition, 2000, Academic Press