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 magistrale in Mathematics - 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
Modules | Credits | TAF | SSD |
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Modules | Credits | TAF | SSD |
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Modules | Credits | TAF | SSD |
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A course to be chosen among the following
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 differential equations (2013/2014)
Teaching code
4S001444
Teacher
Coordinator
Credits
6
Language
English
Scientific Disciplinary Sector (SSD)
MAT/06 - PROBABILITY AND STATISTICS
Period
II semestre dal Mar 3, 2014 al Jun 13, 2014.
Location
VERONA
Learning outcomes
In this course we will introduce the audience to the basic elements of Ito non anticipative stochastic calculus and Stochastic Differential Equations.
Synthetic programme : Brownian Motion, Martingales, Ito integral, Ito formula and martingale representation theorem, strong and weak solutions of a stochastic differential equation, diffusion theory, Feynman Kac formula, application to filtering and stochastic control theory.
Program
Detailed Programme
- Probabilty spaces, random variables, stochastic processes and martingales
- Brownian motion
- Ito integral: construction, properties and extensions
- Ito formula and Martingale representation theorem
- Stochastic differential equations: examples of solution, existence and uniqueness of strong solution, weak solutions, Girsanov theorem and Cameron-Martin formula.
- Diffusion theory : Markov property, generators.
- PDEs problems associated to a diffusion : Dirichlet problem, Parabolic equations, Feynman-Kac formula.
- Application to filtering and stochastic control theory
Examination Methods
Discussion of home works.