Stochastic Processes

his module serves as an introduction to the theory of stochastic processes. It starts with a review of Kolmogorov axioms for probability spaces and continues by providing a rigorous treatment of topics such as independence of events and Borel-Cantelli Lemma, Kolmogorov’s zero-one law, random variables, expected value and variance, the weak and strong laws of large numbers, and the Central limit theorem. More advanced topics that will follow include finite and countable state Markov chains, Galton-Watson trees, and the Wiener process. Several relevant applications that will be discussed are percolation on graphs, application of Markov chains to sampling problems, and probabilistic methods in graph theory. The module also includes examples from mathematical finance.

Assessment

The final grade is based on the final exam. You can imporve your grade by up to 2 grade points (66 percent) by submitting the homework assignments.

Meetings:

Class meets on Thursdays and Fridays, 15:45-17:00.

Textbooks