Duration
20h Th, 10h Pr, 20h Proj.
Number of credits
| Master in mathematics (120 ECTS) | 6 crédits |
Lecturer
Language(s) of instruction
French language
Organisation and examination
Teaching in the first semester, review in January
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
Introduction to stochastic processes and stochastic integration
One-dimensional Brownian Motion
- Motivation
- Multivariate Normal Distribution
- Processes with stationary independent increments
- Brownian Motion : definition
- Brownian Motion : construction
- An overview of path properties
- Markov property and applications
- Continuous time martingales and applications
- Skorokhod embedding (overview)
- Donsker's theorem and applications (overview)
- Basic setup
- From Feller processes to infinitesimal description
- From infinitesimal description to Feller processes
- A few tools
- Applications to Brownian motion
- Motivation
- The Itô integral
- Itô's formula and applications
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 as well as exercise sessions
Mode of delivery (face-to-face ; distance-learning)
Face-to-face
Recommended or required readings
Most of the material is taken from
Liggett, Thomas Milton. Continuous time Markov processes: an introduction. Vol. 113. American Mathematical Soc., 2010.
Additional material from
Steele, J. Michael. Stochastic calculus and financial applications. Vol. 45. Springer Science & Business Media, 2012.
Assessment methods and criteria
Oral examination
Work placement(s)
Organizational remarks
Course taught in English; exercises and exam in French (or English)
Contacts
Université de Liège Département de Mathématique - zone polytech 1 12 allée de la découverte Bât. B37 pkg 33a B-4000 Liège Office : B37 0/68