Martingales Through Measure Theory

(1-3 Credit Hours) · Undergraduate

Probability theory arises in the modelling of a variety of systems where the understanding of the "unknown'' plays a key role, such as population genetics in biology, market evolution in financial mathematics, and learning features in game theory. It is also very useful in various areas of mathematics, including number theory and partial differential equations. The course introduces the basic mathematical framework underlying its rigorous analysis, and is therefore meant to provide some of the tools which will be used in more advanced courses in mathematics. The first part of the course provides a review of measure theory from Integration Part A, and develops a deeper framework for its study. Then we proceed to develop notions of conditional expectation, martingales, and to show limit results for the behavior of these martingales which apply in a variety of contexts.