Duration
30h Th, 10h Pr, 20h Proj.
Number of credits
| Master in mathematics (120 ECTS) (Odd years, organized in 2023-2024) | 8 crédits | |||
| Master in mathematics (60 ECTS) (Odd years, organized in 2023-2024) | 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
I. General notions about stochastic processes
II. Discrete-time stochastic processes and martingales
III. Continuous-time stochastic processes
IV. Definition and construction of the Brownian motion
V. Distribution properties of the Brownian motion
VI. Martingales in continuous time
VII. Sample path properties of the Brownian motion
VIII. Itô Integration
Learning outcomes of the learning unit
The objective is to offer the student the necessary tools to enter a very active but demanding research field.
Prerequisite knowledge and skills
It is compulsory to have a solid background in mathematics (BA in mathematics).
The course "Introduction to Stochastic Processes" is not a pre-requisite.
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
Additional 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.
Recommended or required readings
See French section
Exam(s) in session
Any session
- In-person
oral exam
Written work / report
Additional 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
Contacts
Laurent Loosveldt
Email : l.loosveldt@uliege.be
Département de Mathématique,
Allée de la Découverte, 12, B37,
4000 Liège Belgium
Office 0/59