Foundations of modern probability theory: measure theory, 0/1 laws, independence, conditional expectation with respect to sub sigma algebras, characteristic functions, the central limit theorem, branching processes, discrete parameter martingale theory.
scheda docente
materiale didattico
R. Durrett, Probability: Theory and examples
Testi Adottati
D. Williams, Probability with martingalesR. Durrett, Probability: Theory and examples
Bibliografia Di Riferimento
D. Williams, Probability with martingales R. Durrett, Probability: Theory and examplesModalità Frequenza
Preferably in personModalità Valutazione
The exam consists of two separate parts: the written part and the oral part. In the first one, students will be asked to solve exercises based on the techniques that we have seen in class; 2 hours. The oral part will start with a discussion of the (possible) mistakes that the student did in the first part; afterwards students will be asked to present and comment statements proofs of some of the most important results seen during the lectures.