The aim of the course is to provide students with the basic theoretical tools of the theory of discrete-time stochastic processes, including applications to Markov chains. The result to be achieved at the end of the course is that the student knows how to use the basic techniques of the theory of stochastic processes, having also developed a good intuition on the meaning of the concepts learned.
Course Prerequisites
basics of probability theory
Teaching Methods
Frontal lessons. In the lectures the theoretical notions are developed and the techniques necessary for the application of the theory to the solution of problems in Mathematical Physics are described.
Assessment Methods
Oral test which consists in verifying the ability to express oneself in correct mathematical language and to demonstrate some of the theorems encountered during the course.
Contents
Basics of the abstract theory of measure. Independent and identically distributed random variables. Markov chains. Homogeneous Markov chains. Random walks on groups. Recurrence and transience. Polya’s theorem on randon walks in the n-dimensional integer lattice. Stationary processes, the ergodic theorem, Poincaré recurrence. Irreducible Markov chains and ergodicity.
Course Language
English
More information
to make an appointment write to posilicano@uninsubria.it
