Second Level Degree in Mathematics
Jump second level menu- Courses
- Timetable
- Exams
- Individual study program
- Student seminars
- Thesis
- Thesis Archive
- Graduation dates
- Contacts
STOCHASTIC ANALYSIS - 7 CFU
Teacher
David Barbato
Scheduled Period
I Year - 1 Semester | 04/10/2021 - 15/01/2022
Hours: 56 (24 esercitazione, 32 lezione)
Prerequisites
Basic probability theory, basic analysis (differential calculus in R^d, ordinary differential equations), measure theory.
Target skills and knowledge
The aim of the course is to provide good knowledge of Brownian motion, stochastic integral, Ito's calculus, and stochastic differential equations. During the course some applications and links with the analysis of partial differential equations will be shown.
Examination methods
Th exam consists of two partial part, a written test and oral test.
Assessment criteria
The written test allows access to the oral test. The final evaluation will take into account both tests.
The written test consists of solving exercises whereas the oral test is dedicated to theory (definitions and proofs).
Course contents
Reasons. Stochastic processes (basics).
Probability calculus: notions of convergence, normal multivariate laws, conditional hope.
Brownian motion: construction and main properties.
Discrete and continuous time martingales.
Stochastic integral: construction and properties.
Itô calculation: Itô formula, first applications (e.g. Dirichlet problem), Girsanov's theorem, martingale representation.
Stochastic differential equations: notions of existence and uniqueness, fundamental theorem of existence and uniqueness, examples, Markov properties and diffusions, Feynman-Kac formula.
Planned learning activities and teaching methods
Classroom lessons.
Additional notes about suggested reading
The course material (lessons, exercise sheets and texts of previous assignments) will be uploaded on the moodle website or on teacher website: https://www.math.unipd.it/~barbato/teaching.html