Studying at the University of Verona

Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.

Study Plan

A.A. 2024/2025 A.A. 2023/2024 A.A. 2022/2023 A.A. 2021/2022 A.A. 2020/2021 A.A. 2019/2020 A.A. 2018/2019 A.A. 2017/2018 A.A. 2016/2017 A.A. 2015/2016 A.A. 2014/2015 A.A. 2013/2014 A.A. 2012/2013 A.A. 2011/2012 A.A. 2010/2011 A.A. 2009/2010

This information is intended exclusively for students already enrolled in this course.
If you are a new student interested in enrolling, you can find information about the course of study on the course page:

Laurea in Matematica applicata - Enrollment from 2025/2026

The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.

CURRICULUM TIPO:

1° Year 

ModulesCreditsTAFSSD
12
A
MAT/02 ,MAT/03
12
A
MAT/05
6
A
MAT/08
12
A
FIS/01
12
A
INF/01
6
B
MAT/01

2° Year   activated in the A.Y. 2021/2022

ModulesCreditsTAFSSD
6
A
MAT/02
12
B
MAT/05
6
B
MAT/08
6
B
MAT/03
6
C
SECS-P/01
6
C
SECS-P/01
9
B
MAT/06
6
B
MAT/05
English language B1 level
6
E
-

3° Year   activated in the A.Y. 2022/2023

ModulesCreditsTAFSSD
6
C
SECS-P/05
9
C
SECS-S/06
6
B
MAT/08
6
B
MAT/09
6
B
MAT/06
Final exam
6
E
-
activated in the A.Y. 2021/2022
ModulesCreditsTAFSSD
6
A
MAT/02
12
B
MAT/05
6
B
MAT/08
6
B
MAT/03
6
C
SECS-P/01
6
C
SECS-P/01
9
B
MAT/06
6
B
MAT/05
English language B1 level
6
E
-
activated in the A.Y. 2022/2023
ModulesCreditsTAFSSD
6
C
SECS-P/05
9
C
SECS-S/06
6
B
MAT/08
6
B
MAT/09
6
B
MAT/06
Final exam
6
E
-
Modules Credits TAF SSD
Between the years: 1°- 2°- 3°
12
D
-
Between the years: 1°- 2°- 3°
Other activities
6
F
-

Legend | Type of training activity (TTA)

TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.

A Basic activities
B Characterizing activities
C Related or complementary activities
D Activities to be chosen by the student
E Final examination
F Other training activities
S Placements in companies, public or private institutions and professional associations

Stochastic systems  (2022/2023)

Teaching code

4S00254

Academic staff

Paolo Dai Pra, Francesca Collet

Coordinator

Paolo Dai Pra

Credits

6

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/06 - PROBABILITY AND STATISTICS

Period

Semester 1 dal Oct 3, 2022 al Jan 27, 2023.

Lessons timetable MoodleMoodle Seminars 0

Learning objectives

Moreover a student will be able to analyse some advanced applications of dynamical systems arising from population dynamics, mechanics and traffic flows. Eventually a student will be also able to produce proofs using the typical tools of modern dynamical systems and will be able to read and report specific books and articles on dynamical systems and related applications.

Prerequisites and basic notions

Basics in Probability

Program

1. Conditional expectation and conditional distribution. Martingale. Stopping theorem and convergence theorem.
2. Discrete-time Markov chains. Markov property and transition probability. Irreducibility, aperiodicity. Stationary distributions. Reversible distributions.
3. Hitting times. One step analysis. Convergence to the stationary distribution. Law of large numbers for Markov chains. Markov Chain Monte Carlo methods: Metropolis algorithm and Gibbs sampler.
4. Reducible Markov chains. Transient and recurrent states. Absorption probabilities.
5. Continuous-time Markov chains. The Poisson process and its properties. Continuous-time Markov property. Semigroup associated with a Markov chain: continuity and differentiability; generator. Kolmogorov equations. Stationary distributions. Dynkin's formula. Probabilistic construction of a continuous-time Markov chain.

Bibliography

Vai alla bibliografia
Visualizza la bibliografia con Leganto, strumento che il Sistema Bibliotecario mette a disposizione per recuperare i testi in programma d'esame in modo semplice e innovativo.

Didactic methods

All the topics will be illustrated in class. Additional material, as exercises, lecture notes and further references, will be available on Moodle page of the course.
The rights of students will be preserved in situations of travel limitation or confinement due to national provisions to combat COVID or in particular situations of fragile health. In these cases, you are invited to contact the teacher directly to organize the most appropriate remedial strategies.

Learning assessment procedures

The exam consists of a 180-minute written test. It includes exercises and theoretical questions, with at least one proof of those marked in the course program required.

Students with disabilities or specific learning disorders (SLD), who intend to request the adaptation of the exam, must follow the instructions given HERE

Evaluation criteria

To pass the exam, the student must demonstrate:
-- to have understood the theoretical notions, showing detailed knowledge of definitions and statements, as well as of some proofs;
-- to be able to apply theory to problem-solving.

Exam language

Italiano