- Docente: Massimo Campanino
- Credits: 6
- SSD: MAT/06
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 8208)
Learning outcomes
At the end of the course the student: - has acquired mathematical
bases of Probability Theory at an advanced level and some important
results on sequences of independent variables, stationary
sequences, convergence of probability measures on metrizable
spaces, Fourier transform of probability measures, martingale
theory with discrete time; - he is able to apply acquired knowledge
to the study of stochastic processes.
Course contents
Probability spaces. Probability measures. Rxtension theorem.
Events, random variablea. Expectation and integral. Stochastic
independence. Stationary sequences of random variables. Probability
on metrizable spaces, weak convergence. Fourier transform of
probability measures. Martingales in discrete time.
Readings/Bibliography
N. Pintacuda. Probabilità. Zanichelli.
P. Billingsley. Probability and measure. Wiley.
Teaching methods
The teaching of the course is based on lectures aimed at
providing students with the bases for the study of Probability
Theory at an advanced level, in particular abstract measure theory
and martingale theory, The lectures will be directed at
establishing relations with other areas of mathematics such as
analysis, topology and the theory of dynamical systems
and will be supported by examples and exercises.
Assessment methods
Final verification consists in an oral test.
The oral tests is based on three questions. In answering them the
student will have to show that he/she masters the basic concepts of
the course and that he/she is able to develop rigorous arguments
and to solve simple exercises on the content of the course.
Teaching tools
Lectures.
Office hours
See the website of Massimo Campanino