Anno Accademico 2019/2020
- Docente: Pietro Rigo
- Crediti formativi: 6
- SSD: SECS-S/01
- Lingua di insegnamento: Inglese
- Modalità didattica: Convenzionale - Lezioni in presenza
- Campus: Bologna
- Corso: Laurea Magistrale in Statistical sciences (cod. 9222)
Conoscenze e abilità da conseguire
By the end of the course, the student knows the basic theory of stochastic processes and martingales. On the theoretical side, the student possesses the tools to prove the main results on existence and convergence of conditional expectations and martingales.
Contenuti
Review of a few basic concepts on probability theory
Conditional expectation
General notions about stochastic processes: Definition, paths, filtrations, stopping times, finite dimensional distributions
Existence of processes with given finite dimensional distributions (just an hint)
Martingales
Markov chains
Random walks
Brownian motion
Poisson process (consistently with the available time)
Testi/Bibliografia
Cinlar E. (2011) Probability and stochastic processes, Springer.
Grimmett G. and Stirzaker D. (2001) Probability and random processes, Oxford University Press.
Metodi didattici
Lectures and class exercises
Modalità di verifica e valutazione dell'apprendimento
Oral exam. During the exam, the student may be requested to discuss (not necessarily to solve) some simple exercises together with the teacher. Such exercises are obvious versions of exercises which have been solved in class
Strumenti a supporto della didattica
Notes and the text-books quoted above
Orario di ricevimento
Consulta il sito web di Pietro Rigo