Corsi di Laurea Magistrale in Matematica A.A. 2024/25
Stochastic calculus and applications
Prof. Lorenzo Bertini
The course is divided into various parts. In the first, Brownian
motion will be introduced and its properties discussed, the second
part concerns the general theory of Markov processes (Feller
processes), the third refers properly to stochastic calculus, with the
analysis of stochastic equations. The most interesting part of the
course is the last one in which various applications of the developed
theory are discussed, in particular to statistical physics. Wishes
include: Smoluchowski approximation, McKean-Vlasov system,
Freidlin-Ventzell theory, logarithmic Sobolev inequalities,
Bakry-Emery criterion, stochastic currents,.... Inevitably, they are
largely destined to remain wishes. However, applications to finance
are banned from the course.
Schedule
- Tuesday, 13.00 - 15.00 Classroom G (Dipartimento di Matematica)
- Friday, 10.00 - 12.00 Classroom G (Dipartimento di Matematica)
Meeting: after lectures.
OPIS code: D8P08B0W
Syllabus (tentative)
Examinations schedule
- 16.1.2025
- 07.2.2025
- 17.6.2025
- 04.7.2025
- 10.9.2025
Textbook
-
Thomas M. Liggett,
Continuous Time Markov Processes An Introduction.
American Mathematical Society.
Exercises proposed in the past (in Italian)
Examination procedure (A.A. 2024/25)
The exam consists in a oral interview.
The students have the option to study in more deep one of the topics in
the course, to be agreed with the Professor.
In this case, the first question of the interview will be on that topic.
N.B.
Only the students booked via Infostud will be allowed to take the exam.
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