進階高等機率論

Syllabus:. • Conditional expectations • Gaussian distributions • Martingales • Markov chains • Ergodic theory

The aim of this course is to introduce the advanced topics in probability, which are used in modern mathematics and many other fields of science and engineering. While the choice of topics is motivated by their use in mathematics and various applied areas, the courses will emphasize the theoretical and conceptual underpinnings, just as in other mathematics course Prerequisite: Elements of measure theory

Exams: • Midterm: Wednesday, April 13, 1:20-4:00 p.m., SA 211 . • Final: Wednesday, May 25, 1:20-4:00 p.m., SA 211 . Grading: Midterm exam(50), Final exam(50)

1. Lecture notes for probability theory by Sourav Chatterjee 2. Probability theory by Dmitry Panchenko 3. Lecture notes for integration, probability and random processes by Jean-Francois Le Gall (in French)