- Docente: Pietro Rigo
- Credits: 6
- SSD: SECS-S/01
- Language: English
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Statistical Sciences (cod. 9222)
Learning outcomes
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.
Course contents
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)
Markov chains
Random walks
Brownian motion
Poisson process (consistently with the available time)
Readings/Bibliography
Cinlar E. (2011) Probability and stochastic processes, Springer.
Grimmett G. and Stirzaker D. (2001) Probability and random processes, Oxford University Press.
Teaching methods
Lectures and class exercises
Assessment methods
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
Teaching tools
Notes and the text-books quoted above
Office hours
See the website of Pietro Rigo