The course introduces the abstract theory of probability, but with
constant reference to examples and relevant applications. The main
topics are:
- Probability spaces.
- Laws of large numbers, Central Limit Theorem.
- Markov chains. Percolation.
- Conditional expectations, martingales.
- Brownian motion.
R. Durrett, Probability and Examples. 4th edition, Cambridge Univ. Press,
2010.
- Note del docente
Learning Objectives
Knowledge acquired: the successful student has a basic knowledge of
probability theory and of several examples and applications. In particular
he/she knows the foundations of probability both in the discrete (Markov
chains, percolation) and in the continuous (Brownian motion) setting.
Competence acquired: the successful student is able to rigorously solve
several problems about determining probabilities and selection models.
He/she can also rigorously operate with probability spaces, random
variables, Markov chains, martingales.
Prerequisites
Courses required: Probabilità e Statistica (Introduction to probability and
statistics 6-9 cfu). Analisi Matematica II (Mathematical Analysis II -
multivariate calculus)
Courses recommended: Analisi Matematica III (Mathematical analysis III -
Lebesgue integration)
Teaching Methods
Number of hours for personal study and other individual learning: 153
Number of hours for classroom activities: 72
Further information
Frequency of lessons and exercises: Not required
Tools for Teaching:
http://web.math.unifi.it/users/gandolfi/didindex.html
Office hours:
by appointment
address:
Viale Morgagni, 67 / A - 50134 Florence
Tel: 055 4237478
Fax: 055 4237165
E-mail: @ alberto.gandolfi unifi.it gandolfi@math.unifi.it
Web: http://web.math.unifi.it/users/gandolfi/
Type of Assessment
Oral exam
Course program
The course introduces the abstract theory of probability, but with
constant reference to examples and relevant applications. The main
topics are:
- Probability spaces.
- Laws of large numbers, Central Limit Theorem.
- Markov chains. Percolation.
- Conditional expectations, martingales.
- Brownian motion.