What it is about
You will learn the measure-theoretic probability theory for sequences of random variables and martingales. By the end you will be able to understand and apply central results such as the law of large numbers, central limit theorems, and fundamental martingale results.
What you will be able to do
- Understanding measure-theoretic concepts in probability theory
- Applying laws for sequences of i.i.d. random variables (LLN, CLT)
- Familiarity with convergence concepts and characteristic functions
- Mastery of the fundamentals of martingale theory and important theorems
What the module consists of
- VorlesungTransmission of theoretical content with examples and discussion
- Übung/Practice sessionsConsolidation through problem sheets, solutions and supervised/independent work
Teaching method
- Lecture with examples and discussionpresents content, motivates independent study
- Supervised, increasingly autonomous practice sessionsenable deepening, practice and self-assessment