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.
Type D and Type F activities
Type D learning activities are the student's choice, type F activities are additional knowledge useful for job placement (internships, transversal skills, project works, etc.). According to the Teaching Regulations of the Course, some activities can be chosen and entered independently in the booklet, others must be approved by a special committee to verify their consistency with the study plan. Type D or F learning activities can be covered by the following activities.
1. Modules taught at the University of Verona
Include the modules listed below and/or in the Course Catalogue (which can also be filtered by language of delivery via Advanced Search).
Booklet entry mode: if the teaching is included among those listed below, the student can enter it independently during the period in which the curriculum is open; otherwise, the student must make a request to the Secretariat, sending the form to carriere.scienze@ateneo.univr.it during the period indicated.
2. CLA certificate or language equivalency
In addition to those required by the curriculum/study plan, the following are recognized for those matriculated from A.Y. 2021/2022:
- English language: 3 CFUs are recognized for each level of proficiency above that required by the course of study (if not already recognized in the previous course of study).
- Other languages and Italian for foreigners: 3 CFUs are recognized for each proficiency level starting from A2 (if not already recognized in the previous study cycle).
These CFUs will be recognized, up to a maximum of 6 CFUs in total, of type F if the study plan allows it, or of type D. Additional elective credits for language knowledge may be recognized only if consistent with the student's educational project and if adequately justified.
Those enrolled until A.Y. 2020/2021 should consult the information found here.
Method of inclusion in the booklet: request the certificate or equivalency from CLA and send it to the Student Secretariat - Careers for the inclusion of the exam in the career, by email: carriere.scienze@ateneo.univr.it
3. Transversal skills
Discover the training paths promoted by the University's TALC - Teaching and learning center intended for students regularly enrolled in the academic year of course delivery https://talc.univr.it/it/competenze-trasversali
Mode of inclusion in the booklet: the teaching is not expected to be included in the curriculum. Only upon obtaining the Open Badge will the booklet CFUs be automatically validated. The registration of CFUs in career is not instantaneous, but there will be some technical time to wait.
4. CONTAMINATION LAB
The Contamination Lab Verona (CLab Verona) is an experiential course with modules on innovation and enterprise culture that offers the opportunity to work in teams with students from all areas to solve challenges set by companies and organisations.
Upon completion of a CLab, students will be entitled to receive 6 CFU (D- or F-type credits).
Find out more: https://www.univr.it/clabverona
PLEASE NOTE: In order to be admitted to any teaching activities, including those of your choice, you must be enrolled in the academic year in which the activities in question are offered. Students who are about to graduate in the December and April sessions are therefore advised NOT to undertake extracurricular activities in the new academic year in which they are not enrolled, as these graduation sessions are valid for students enrolled in the previous academic year. Therefore, students who undertake an activity in an academic year in which they are not enrolled will not be granted CFU credits.
5. Internship/internship period
In addition to the CFUs stipulated in the curriculum/study plan (check carefully what is indicated on the Teaching Regulations): here information on how to activate the internship.
Check in the regulations which activities can be Type D and which can be Type F.
Modules and other activities that can be entered independently in the booklet
years | Modules | TAF | Teacher | |
---|---|---|---|---|
1° | Genetics | D |
Massimo Delledonne
(Coordinator)
|
|
1° 2° | Algorithms | D |
Roberto Segala
(Coordinator)
|
|
1° 2° | Introduction to Docker | D |
Franco Fummi
(Coordinator)
|
|
1° 2° | Mobile app design by using React Native | D |
Graziano Pravadelli
(Coordinator)
|
years | Modules | TAF | Teacher |
---|---|---|---|
1° 2° | Algorithms | D |
Roberto Segala
(Coordinator)
|
1° 2° | LaTeX Language | D |
Enrico Gregorio
(Coordinator)
|
1° 2° | Python programming language | D |
Carlo Combi
(Coordinator)
|
1° 2° | Organization Studies | D |
Serena Cubico
(Coordinator)
|
1° 2° | History and Didactics of Geology | D |
Guido Gonzato
(Coordinator)
|
years | Modules | TAF | Teacher |
---|---|---|---|
1° 2° | ECMI modelling week | F | Not yet assigned |
1° 2° | ESA Summer of code in space (SOCIS) | F | Not yet assigned |
1° 2° | Federated learning from zero to hero | D |
Gloria Menegaz
|
1° 2° | Google summer of code (GSOC) | F | Not yet assigned |
1° 2° | Mathematics mini courses |
Paolo Dai Pra
(Coordinator)
|
Stochastic Calculus (2022/2023)
Teaching code
4S008268
Teacher
Coordinator
Credits
6
Language
English
Scientific Disciplinary Sector (SSD)
MAT/06 - PROBABILITY AND STATISTICS
Period
Semester 2 dal Mar 6, 2023 al Jun 16, 2023.
Learning objectives
This course will provide an introduction to the theory of Stochastic Differential Equations (SDEs), mainly based on the Brownian motion type of noise. The purpose of this course is to introduce and analyse probability models that capture the stochastic features of the system under study to predict the short and long term effects that this randomness will have on the systems under consideration. The study of probability models for continuous-time stochastic processes involves a broad range of mathematical and computational tools. This course will strike a balance between the mathematics and the applications. The main applications will be mathematical finance, biology and populations evolution, also with respect to their descriptions in terms of the associated SDEs. Topics include: construction of Brownian motion; martingales in continuous time; stochastic integral; Ito calculus; stochastic differential equations; Girsanov theorem; martingale representation; the Feynman-Kac formula and Lévy processes.
Prerequisites and basic notions
Basic tools of probability calculus, eg: definition of discrete / continuous random variables,, central limit theorem, discrete / continuous time Markov chains.
Program
* Probability essential recalls
* SP: definitions/main properties recall ; Martingales ; Option Sampling Theorem ; Quadratic Variation ;
* Stochastic processes at discrete time: recalls and emphasis on random walk (starting from the binomial model, also in more than 1 dimension);
* Different constructions of the Brownian motion: Kolmogorov Consistency Theorem / Kolmogorov-
Cénstor Th.eorem;
* Properties of the Brownian motion
* Derivation/construction of the Stochastic Integral(s) notion(s)
* Ito-Doeoblin rule: Levy's Criteria / Martingale Representation
* Stratonovich approach / Ito representation Theorem (applications/examples)
* Markov processes and relation(s) with the Brownian motion sp [further Bm's properties]
* Girsanov formula / Cameron-Martin (Girsanov) Theorem and Exponential Martingales
* Construction and rigorous derivation of Stochastic Differential Equations
* Strong solutions / Gronwall Lemma / Weak solutions (for SDEs)
* Diffusions / Semi-group approach / Markov property(ies)
* Dynkin's formula / Kolmogorov equation(s) / Feynman-Kac theorem
* Interplay between PDEs and SPDEs (via F-K theorem)
* SDEs application w.r.t. the Financial framework
Bibliography
Didactic methods
Lectures with sharing of slides, lecture notes, specific bibliographic references for particular theoretical insights.
Learning assessment procedures
Oral exam with written exercise:
the exam is based on open questions and/or on the presentation of a project agreed with the course professor and or on the resolution of written exercises to be solved during the test itself. Questions, open-ended and exercises, aim at verify the knowledge about arguments developed within the course, the solution of related concrete problems as well as to verify the acquired acquaintance using stochastic analysis tools.
Evaluation criteria
Evaluation of the understanding and ability to use of the main tools of stochastic analysis, with emphasis on their rigorous definition / analytical derivation.
Criteria for the composition of the final grade
The final grade is the result of the evaluation of the final oral exam, with the possible inclusion of ongoing assessments relating to projects (optional) carried out by the student.
Exam language
Inglese / English