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.

A.A. 2015/2016

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, 2015 Jan 29, 2016
II semestre Mar 1, 2016 Jun 10, 2016
Exam sessions
Session From To
Sessione straordinaria Appelli d'esame Feb 1, 2016 Feb 29, 2016
Sessione estiva Appelli d'esame Jun 13, 2016 Jul 29, 2016
Sessione autunnale Appelli d'esame Sep 1, 2016 Sep 30, 2016
Degree sessions
Session From To
Sess. autun. App. di Laurea Oct 12, 2015 Oct 12, 2015
Sess. autun. App. di Laurea Nov 26, 2015 Nov 26, 2015
Sess. invern. App. di Laurea Mar 15, 2016 Mar 15, 2016
Sess. estiva App. di Laurea Jul 19, 2016 Jul 19, 2016
Sess. autun. 2016 App. di Laurea Oct 11, 2016 Oct 11, 2016
Sess. autun 2016 App. di Laurea Nov 30, 2016 Nov 30, 2016
Sess. invern. 2017 App. di Laurea Mar 16, 2017 Mar 16, 2017
Holidays
Period From To
Festività dell'Immacolata Concezione Dec 8, 2015 Dec 8, 2015
Vacanze di Natale Dec 23, 2015 Jan 6, 2016
Vacanze Pasquali Mar 24, 2016 Mar 29, 2016
Anniversario della Liberazione Apr 25, 2016 Apr 25, 2016
Festa del S. Patrono S. Zeno May 21, 2016 May 21, 2016
Festa della Repubblica Jun 2, 2016 Jun 2, 2016
Vacanze estive Aug 8, 2016 Aug 15, 2016

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 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

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)
One course to be chosen among the following
6
C
(SECS-P/01)
6
C
(FIS/01)
6
B
(MAT/03)
One course to be chosen among the following
6
C
(SECS-P/01)
6
B
(MAT/06)
ModulesCreditsTAFSSD
One/two courses to be chosen among the following
12
C
(SECS-S/06)
6
C
(MAT/07)
6
C
(SECS-P/05)
Prova finale
6
E
(-)

2° Year

ModulesCreditsTAFSSD
6
A
(MAT/02)
One course to be chosen among the following
6
C
(SECS-P/01)
6
C
(FIS/01)
6
B
(MAT/03)
One course to be chosen among the following
6
C
(SECS-P/01)
6
B
(MAT/06)

3° Year

ModulesCreditsTAFSSD
One/two courses to be chosen among the following
12
C
(SECS-S/06)
6
C
(MAT/07)
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°
Other activitites
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

Coordinatore

Luca Di Persio

Scientific Disciplinary Sector (SSD)

MAT/06 - PROBABILITY AND STATISTICS

Language

Italian

The teaching is organized as follows:

Analisi di serie temporali

Credits

2

Period

I semestre

Academic staff

Luca Di Persio

Catene di Markov in tempo discreto

Credits

3

Period

I semestre

Academic staff

Luca Di Persio

esercitazioni

Credits

1

Period

I semestre

Academic staff

Marco Caliari

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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.

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.

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

Gestione carriere


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.