Academic Year 2019/2020

  • 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. Extension theorem. Events, random variables. 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.

R. L. Schilling. Measures integrals and martingales. 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 goal is to ascertain the knowledge of the concepts, the comprehension of the relation between the topics that are developed  and of the proofs of the main results. Moreover the capacity of solving simple exercises related to the topics of the course will be tested. 

Teaching tools

Lectures.

Office hours

See the website of Massimo Campanino