Introdution to Stochastic Methods

Foundations and methods of stochastic processes: random number generation and sampling; random variables, expectation, and the laws of large numbers and the central limit theorem; variance reduction and Monte Carlo integration; discrete- and continuous-time Markov chains; Poisson processes; random walks and diffusion; and Markov-chain Monte Carlo, with applications to networks, optimisation, and statistical inference.

The course introduces the modelling and analysis of randomness in dynamical and data-generating systems. By the end, students can formulate stochastic models, reason about their limiting behaviour, and apply Monte Carlo and Markov-chain techniques to problems in inference, optimisation, networks, and simulation.

In presenza

Lectures developing the theory alongside simulation-based illustration, weekly exercise sessions, and computational assignments in which students implement and analyse stochastic methods on concrete problems.

Assessment is based on quizzes, exams, and projects.