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
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 2025/2026The 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.
1° Year
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2° Year activated in the A.Y. 2013/2014
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One course chosen from the following two
3° Year activated in the A.Y. 2014/2015
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One course of 12 ECTS or two courses of 6 ECTS chosen from the following three
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Modules | Credits | TAF | SSD |
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One course chosen from the following two
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One course of 12 ECTS or two courses of 6 ECTS chosen from the following three
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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.
Stochastic systems (2014/2015)
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
Analisi di serie temporali
Esercitazioni
Learning outcomes
The course is split into three parts.
Module 1 (Discrete-time Markov Chains, Prof. Dai Pra)
The course provides an introduction to discrete-time Markov chain, with finite or countable state space
Module 2 (Practice of Stochastic Systems, Dott. Caliari)
Exercises and practice on Module 1, see web page.
Module 3 (Temporal series analysis, Dott. Di Palma)
Theory for the analysis of discrete time temporal series.
Program
Module 1
- Introduction to finite-state Markov chain: irreducibility, periodicity, stationary distributions, classification of states. Examples.
- Markov chain Monte Carlo. Perfect simulation.
- Convergence to equilibrium of Markov chains. Mixing time. Ergodic Theorem. Coupling methods. Strong stationary times.
- Martingales: optional stoppini theorem, harmonic functions.
- Markov chains with countable state space: recurrence and transience.
- Approximation of invatiant measures.
- Metropolis' algorithm
- Queue simulation
Examination Methods
Module 1: written examination.
Module 2: oral discussion about homeworks.
Module 3: oral discussion of a given project.
The final mark is the weighted average of the three.
Teaching materials e documents
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Modulo 3:0 - Informazioni sul corso (it, 123 KB, 11/19/14)
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Modulo 3:1 - Modelli: tassonomia, principali modelli lineari (ARX, MA, AR ed OE), famiglia generale di modelli, predittore ottimo (it, 141 KB, 11/19/14)
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Modulo 3:2 - Identificazione: definizione del problema, principali criteri (PEM, LS e ML), errore di stima (it, 157 KB, 11/19/14)
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Modulo 3:3 - Validazione: definizione del problema, SSR, corss-validazione ed analisi dei residui (test di cambio dei segni) (it, 128 KB, 11/26/14)
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Modulo 3:4 - DoE: principali segnali di ingresso (Rumore Bianco, Gradino, Rampa) e requisiti (it, 72 KB, 11/26/14)
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Modulo 3:Esercitazione 1 - Predizione & Simulazione (it, 1316 KB, 11/19/14)
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Modulo 3:Esercitazione 2 - Metodi ad errore di predizione (it, 675 KB, 11/19/14)
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Modulo 3:Esercitazione 3 - Validazione (it, 1194 KB, 11/26/14)
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Modulo 3:Esercitazione 4 - Simulazione esame (it, 666 KB, 11/26/14)
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Dispense/Lecture Notes Modulo 2 (it, 183 KB, 10/14/14)