Stochastic Methods in Mathematical Modelling (MA060363)

(10/27/2021-12/21/2021)

Course Memo

Stochastic processes play an important role in natural sciences, computational theory as well as in sampling and synthetic data generation for machine learning. The course aims to cover basic methods of stochastic modelling, such as: Monte-Carlo methods, the modelling of scale-free phenomena as well as stochastic optimisation approaches. The first part of the course provides an introduction to the methods of description and generation of randomness. The main idea is to establish a firm ground for more advanced topics and to help students feel comfortable with advanced machine learning courses. A special emphasis is put on the ubiquitous scale-free and non-gaussian stochastic processes also known as anomalous diffusion. Different causes of these processes will be discussed with examples such as practically important class of first-passage problems. The second half of the course will deal with Monte-Carlo algorithms, inference and learning, classical random network theory, Markov decision processes and stochastic optimal control.