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.

Academic calendar

The academic calendar shows the deadlines and scheduled events that are relevant to students, teaching and technical-administrative staff of the University. Public holidays and University closures are also indicated. The academic year normally begins on 1 October each year and ends on 30 September of the following year.

Academic calendar

Course calendar

The Academic Calendar sets out the degree programme lecture and exam timetables, as well as the relevant university closure dates..

Definition of lesson periods
Period From To
I semestre Oct 1, 2013 Jan 31, 2014
II semestre Mar 3, 2014 Jun 13, 2014
Exam sessions
Session From To
Sessione straordinaria Feb 3, 2014 Feb 28, 2014
Sessione estiva Jun 16, 2014 Jul 31, 2014
Sessione autunnale Sep 1, 2014 Sep 30, 2014
Degree sessions
Session From To
Sessione autunnale Oct 15, 2013 Oct 15, 2013
Sessione straordinaria Dec 9, 2013 Dec 9, 2013
Sessione invernale Mar 18, 2014 Mar 18, 2014
Sessione estiva Jul 21, 2014 Jul 21, 2014
Holidays
Period From To
Vacanze Natalizie Dec 22, 2013 Jan 6, 2014
Vacanze di Pasqua Apr 17, 2014 Apr 22, 2014
Festa del S. Patrono S. Zeno May 21, 2014 May 21, 2014
Vacanze Estive Aug 11, 2014 Aug 15, 2014

Exam calendar

Exam dates and rounds are managed by the relevant Science and Engineering Teaching and Student Services Unit.
To view all the exam sessions available, please use the Exam dashboard on ESSE3.
If you forgot your login details or have problems logging in, please contact the relevant IT HelpDesk, or check the login details recovery web page.

Exam calendar

Should you have any doubts or questions, please check the Enrolment FAQs

Academic staff

A B C D G L M O R S Z

Angeleri Lidia

lidia.angeleri@univr.it 045 802 7911

Baldo Sisto

sisto.baldo@univr.it 045 802 7935

Bos Leonard Peter

leonardpeter.bos@univr.it +39 045 802 7987

Caliari Marco

marco.caliari@univr.it +39 045 802 7904

Daffara Claudia

claudia.daffara@univr.it +39 045 802 7942

Daldosso Nicola

nicola.daldosso@univr.it +39 045 8027076 - 7828 (laboratorio)

De Sinopoli Francesco

francesco.desinopoli@univr.it 045 842 5450

Di Persio Luca

luca.dipersio@univr.it +39 045 802 7968
Foto,  April 11, 2016

Dos Santos Vitoria Jorge Nuno

jorge.vitoria@univr.it

Gaburro Elena

elena.gaburro@unitn.it, elenagaburro@gmail.com

Gobbi Bruno

bruno.gobbi@univr.it

Magazzini Laura

laura.magazzini@univr.it 045 8028525

Malachini Luigi

luigi.malachini@univr.it 045 8054933

Marigonda Antonio

antonio.marigonda@univr.it +39 045 802 7809

Mariotto Gino

gino.mariotto@univr.it +39 045 8027031

Mariutti Gianpaolo

gianpaolo.mariutti@univr.it 045 802 8241

Mazzuoccolo Giuseppe

giuseppe.mazzuoccolo@univr.it +39 0458027838

Orlandi Giandomenico

giandomenico.orlandi at univr.it 045 802 7986

Rizzi Romeo

romeo.rizzi@univr.it +39 045 8027088

Sansonetto Nicola

nicola.sansonetto@univr.it 049-8027932

Schuster Peter Michael

peter.schuster@univr.it +39 045 802 7029

Solitro Ugo

ugo.solitro@univr.it +39 045 802 7977
Marco Squassina,  January 5, 2014

Squassina Marco

marco.squassina@univr.it +39 045 802 7913

Zampieri Gaetano

gaetano.zampieri@univr.it +39 045 8027979

Zuccher Simone

simone.zuccher@univr.it

Study Plan

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 enrolment year.

ModulesCreditsTAFSSD
6
A
MAT/02
Uno tra i seguenti insegnamenti
6
C
SECS-P/01
6
C
FIS/01
6
B
MAT/03
Uno tra i seguenti insegnamenti
6
C
SECS-P/01
6
B
MAT/06
ModulesCreditsTAFSSD
Uno o due insegnamenti tra i seguenti per un totale di 12 cfu
6
C
SECS-P/05
Prova finale
6
E
-

2° Year

ModulesCreditsTAFSSD
6
A
MAT/02
Uno tra i seguenti insegnamenti
6
C
SECS-P/01
6
C
FIS/01
6
B
MAT/03
Uno tra i seguenti insegnamenti
6
C
SECS-P/01
6
B
MAT/06

3° Year

ModulesCreditsTAFSSD
Uno o due insegnamenti tra i seguenti per un totale di 12 cfu
6
C
SECS-P/05
Prova finale
6
E
-
Modules Credits TAF SSD
Between the years: 1°- 2°- 3°
Between the years: 1°- 2°- 3°
Ulteriori conoscenze
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.




SPlacements in companies, public or private institutions and professional associations

Teaching code

4S00254

Credits

6

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/06 - PROBABILITY AND STATISTICS

The teaching is organized as follows:

Catene di Markov in tempo discreto

Credits

3

Period

I semestre

Academic staff

Luca Di Persio

Analisi di serie temporali

Credits

2

Period

I semestre

Academic staff

Luca Di Persio

esercitazioni

Credits

1

Period

I semestre

Academic staff

Marco Caliari

Learning outcomes

The Stochastic Systems course aims at giving an introduction to the basic concepts underlying the rigorous mathematical description of the temporal dynamics for random quantities.

The course prerequisites are those of a standard course in Probability, for Mathematics / Physics.

It is supposed that students are familiar with the basics Probability calculus, in the Kolmogorov assiomatisation setting, in particular with respect to the concepts of density function, probability distribution, conditional probability, conditional expectation for random variables, measure theory (basic ), characteristic functions of random variables, etc.

The Stochastic Systems course aims, in particular, to provide the basic concepts of: Filtered probability space, martingale processes, stopping times, Doob theorems, theory of Markov chains in discrete and continuous time (classification of states, invariant and limit,measures, ergodic theorems, etc.), basics on queues theory and an introduction to Brownian motion.

A part of the course is devoted to the computer implementation of operational concepts underlying the discussion of stochastic systems of the Markov chain type, both in discrete and continuous time.

A part of the course is dedicated to the introduction and the operational study, via computer simulations, to univariate time series.

Program

Stochastic Systems [ Applied Mathematics ]
AA 2015/2016

Syllabus

• Conditional Expectetion ( from Chap.1 of [BMP] )
• Definitions and basic properties
• Conditional expectations and conditional laws

• Introduction to stochastic processes ( From Chap.1 di [BMP] )
• Filtered probability space, filtrations
• Adapted stochastic process (wrt a given filtration)
• Martingale (first definitions and examples: Markov chains)
• Kolmogorov characterization theorem
• Stopping times

• Martingale ( From Chap.3 of [BMP]
• Definition of martingale process, resp. super, resp. lower, martingale
• Fundamental properties
• Stopping times for martingale processes
• Convergence theorems for martingales

• Markov chains (MC) ( From Chap.4 of [Beichelet] , Chap.5 of di [Baldi] )
• Transition matrix for a MC
• Construction and existence for MC
• Omogeneous MC (with respect to time and space)
• Canonical MC
• Classification of states for a given MC ( and associated classes )
• Chapman-Kolmogorov equation
• Recurrent, resp. transient, states ( classification criteria )
• Irriducible and recurrent chains
• Invariant (stationary) measures, ergodic measures, limit measures ( Ergodic theorem )
• Birth and death processes (discrete time)

• Continuous time MC ( From Chap.5 of [Beichelt] )
• Basic definitions
• Chapman-Kolmogorov equations
• Absolute and stationary distributions
• States classifications
• Probability and rates of transition
• Kolmogorov differential equations
• Stationary laws
• Birth and death processes ( first steps in continuous time )
• Queque theory (first steps in continuous time)

• Point, Counting and Poisson Processes ( From Chap.3 of [Beichelt] )
• Basic definitions and properties
• Stochastic point processes (SPP) and Stochastic Counting Processes (SCP)
• Marked SPP
• Stationarity, intensity and composition for SPP and SCP
• Homogeneous Poisson Processes (HPP)
• Non Homogeneous Poisson Processes (nHPP)
• Mixed Poisson Processes (MPP)

• Birth and Death processes (B&D) ( From Chap.5 of [Beichelt] )
• Birth processes
• Death processes
• B&D processes
° Time-dependent state probabilities
° Stationary state probabilities
° Inhomogeneous B&D processes

• An introduction to quequing theory (From Chap.5 of [Beichelt] )
• Basic concepts
• Classification A/B/s/m by Kendall
• Explicitly studied examples:
° M/M/+\infty
° M/M/s/0
# partial results for M/M/+\infty e M/G/+\infty
° M/M/s/+\infty
• Erlang's loss formula
• Little's formula


• Brownian Motion (BM) ( From Chap.7 of [Beichelt] )
• Definitions and basic properties
• Transformations of 1-dimensional BM
° exponential martingale
° variance martingale


Bibliography

Text used in the course are:

[Baldi] P. Baldi, Calcolo delle Probabilità, McGraw-Hill Edizioni (Ed. 01/2007)

[Beichelt] F. Beichelt, Stochastic Processes in Science, Engineering and Finance, Chapman & Hall/CRC, Taylor & Francis group, (Ed. 2006)

[BPM] P. Baldi, L. Matzliak and P. Priouret, Martingales and Markov Chains – Solve Exercises and Elements of Theory, Chapman & Hall/CRC (English edition, 2002)


Further interesting books are:

N. Pintacuda, Catene di Markov, Edizioni ETS (ed. 2000)

Brémaud, P., Markov Chains. Gibbs Fields, Monte Carlo Simulation, and Queues, Texts in Applied Mathematics, 31. Springer-Verlag, New York, 1999

Duflo, M., Random Iterative Models, Applications of Mathematics, 34. SpringerVerlag, Berlin, 1997

Durrett, R., Probability: Theory and Examples, Wadsworth and Brooks, Pacific Grove CA, 1991

Grimmett, G. R. and Stirzaker, D. R., Probability and Random Processes. Solved Problems. Second edition. The Clarendon Press, Oxford University Press, New York, 1991

Hoel, P. G., Port, S. C. and Stone, C. J., Introduction to Stochastic Processes, Houghton Mifflin, Boston, 1972

Examination Methods

The course is diveded into the following three parts

1) Theory of stochastic systems
2) Introduction to time-series analysis
3) Computer exercises ( mainly based on the theory of Markov Chains, in discrete as well in continuous time )

The exam will be subdivided into the following three parts

* a written exam concerning point (1)
* a project presented in agreement with the programme developed with prof. Marco Caliari (point 3)
* exercises and a project concerning point (2)

The programme concerning the written exam, with respect to point (1), is the one reported in the Program section.
The project to be presented with prof. Caliari has to be decided with him.
The project to be presented with respect to point (2), will be chosen, by each student, within the the following list

========
Projects
========

1-Compare the following methods of estimate and/or elimination of time series trends

*First order differences study
*Smoothing with moving average filter
*Fourier transform
*Exponential Smoothing
*Polynomial Data fitting

2- Describe and provide a numerical implementation of the one-step predictor for the following models

FIR(4)
ARX(3,1)
OE(3,1)
ARMA(2,3)
ARMAX(2,1,2)
Box-Jenkins(nb,nc,nd,nf)

3- Compare the Prediction Error Minimization (PEM) and the Maximum Likelihood (ML) approach for the identification of the model parameters (it requires a personal effort in the homes ML)

4- Provide a concrete implementation for the k-fold cross-validation, e.g. using Matlab/Octave, following the example-test that has been given during the lessons

5-Detailed explanation of (at least) one of the following test
*Shapiro-Wilk
*Kolmogorov-Smirnov
*Lilliefors

Type D and Type F activities

Modules not yet included

Career prospects


Module/Programme news

News for students

There you will find information, resources and services useful during your time at the University (Student’s exam record, your study plan on ESSE3, Distance Learning courses, university email account, office forms, administrative procedures, etc.). You can log into MyUnivr with your GIA login details.

Further services

I servizi e le attività di orientamento sono pensati per fornire alle future matricole gli strumenti e le informazioni che consentano loro di compiere una scelta consapevole del corso di studi universitario.


Graduation

Attachments

List of theses and work experience proposals

theses proposals Research area
Formule di rappresentazione per gradienti generalizzati Mathematics - Analysis
Formule di rappresentazione per gradienti generalizzati Mathematics - Mathematics
Mathematics Bachelor and Master thesis titles Various topics
Stage Research area
Internship proposals for students in mathematics Various topics

Attendance

As stated in point 25 of the Teaching Regulations for the A.Y. 2021/2022, except for specific practical or lab activities, attendance is not mandatory. Regarding these activities, please see the web page of each module for information on the number of hours that must be attended on-site.
Please refer to the Crisis Unit's latest updates for the mode of teaching.

Career management


Area riservata studenti