5.00 credits
30.0 h
Q2
Teacher(s)
Hainaut Donatien;
Language
French
> English-friendly
> English-friendly
Prerequisites
The courses MAT1322 Measurement Theory and MAT1371 Probability are an absolute prerequisite
Main themes
Processes, martingales et Markov chain in discrete and continuous time. Stopping times. Poisson Process, Brownian motian and Itô calculus
Learning outcomes
At the end of this learning unit, the student is able to : | |
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Content
This course is a detailled introduction to stochastic processes in discrete and continuous time:
Part I:
Part I:
- Revision of probability theory
- Martingales in discrete time
- Markov Chaine in discrete time and with a finite number of states
- Poisson processes and Poisson measures
- Continuous Markov process with a finite number of states
- Brownian motien & Itô's calculus
- Continuous time martingales
- Continuous Markov processes with infinite number of state
Teaching methods
15 lectures of 2 hours
Evaluation methods
Written exam
Other information
A first course in probability and statistics : "LMAT1271 Calcul des probabilités et analyse statistique" or equivalent, and eventually "LMAT1371 Théorie des probabilités".
Online resources
Lecture notes are available on Moodle
Bibliography
- NEVEU, J., Martingales à temps discret, Masson, 1972. BREIMAN, L., Probability, Addison-Wesley, 1968.
- CHOW, Y.S. and M. TEICHER, Probability Theory: Independence, Interchangeability, Martingales, Springer-Verlag, 1987.
- CHUNG K.L., A Course in Probability Theory. Harcourt, Brace & World Inc., 1968.
- KARLIN S. and H.M. TAYLOR, A First Course in Stochastic Processes, Academic Press, 1975.
Teaching materials
- matériel sur moodle
Faculty or entity
MATH
