Duration
30h Th, 10h Pr, 20h Proj.
Number of credits
| Master in mathematics, research focus (Even years, organized in 2024-2025) | 8 crédits | |||
| Master in mathematics, teaching focus (Even years, organized in 2024-2025) | 8 crédits |
Lecturer
Language(s) of instruction
French language
Organisation and examination
Teaching in the second semester
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
The study of stochastic processes and the associated stochastic analysis are among the most contemporain domains in mathematics. They are still on the rise. The objective of this course is to offer the student the necessary tools to enter a very active but demanding research field.
In this course, we present the stochastic analysis built starting from an isonormal process. This general approach will be illustrated with processes which are commonly used in practice such as Brownian motion, Brownian field or Brownian sheet.
Depending on the affinity of the students and time available, various fondamental subjects from stochastic analysis could be discussed, such as
- stochastic integration
- Malliavin calculus
- Wiener chaos
- chaotic stochastic processes
- stochastic differential equations
- quantitative versions of the Central Limit Theorem
- ...
Learning outcomes of the learning unit
The student will be able to understand the fundamental notions of stochastic analysis and start the study of harder subjets in this direction.
Prerequisite knowledge and skills
It is compulsory to have a solid background in mathematics (BA in mathematics).
Planned learning activities and teaching methods
Ex cathedra classes, exercice sessions and a personal work.
Mode of delivery (face to face, distance learning, hybrid learning)
Face-to-face course
Further information:
The theory will be presented during "face-to-face" lectures.
Students will have to solve exercises, alone or by group, and these exercises will be corrected and discuted during lectures.
Course materials and recommended or required readings
Platform(s) used for course materials:
- eCampus
- MyULiège
Further information:
Course notes will be made available on e-campus, depending on the progress of their redaction
Exam(s) in session
Any session
- In-person
oral exam
Written work / report
Further information:
An oral examination consisting of theory and exercises will be organized. A personal work, which must be submitted one week before the exam, will also be requested.
Work placement(s)
Organisational remarks and main changes to the course
Course taught in French every two years.
This course is organised every two years on a rolling basis with MATH0079-1 - Stochastic processes. Even it is interesting to take both courses (during the two years of the master) to get a larger knownledge in stochastic analysis, the content of both courses are thought in such a way that they are independent.
Contacts
Laurent Loosveldt
Institut de Mathématique - B37 - Bureau 0/59
Quartier Polytech 1
Allée de la découverte, 12
4000 Liège (Sart-Tilman)
Tél. : (04) 366.92.56.
E-mail : l.loosveldt@uliege.be