20h Th, 10h Pr, 10h Mon. WS
Number of credits
|Bachelor in computer science||5 crédits|
|Master in data science (120 ECTS)||5 crédits|
|Master of science in computer science and engineering (120 ECTS)||5 crédits|
|Bachelor in mathematics||4 crédits|
Language(s) of instruction
Organisation and examination
Teaching in the second semester
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
Markov chains in discrete time (definition, classification of states, absorption time, strong Markov property, recurrence and transience, invariant distributions, convergence to equilibrium). Markov chains in continuous time (Q-matrices and exponential, Poisson process, life and death processes, properties of Markov chains in continuous time, classification of states, recurrence and transience, invariant distribution, convergence to equilibrium ). Queues (Kendall notation, occupancy rates, performance metrics, file M / M / m).
Learning outcomes of the learning unit
After the course, students will master the main properties of most classical stochastic processes.
Prerequisite knowledge and skills
Basic probability theory. Elementary notions of calculus and linear algebra. Understanding of R and/or Matlab.
Planned learning activities and teaching methods
In addition to the traditional classroom course, the course includes 10 hours traditional exercise sessions (10h Pr, ex cathedra).
Students from the Mathematic Department will also have 10 hours of personal research work (10h TD). This work will be carried out in groups, in ways yet to be determined (responsible : Prof. Pierre Geurts)
Students from Montefiore will also have 30 hours of personal research work (30h TD). This work will be carried out in groups, in ways yet to be determined (responsible : Prof. Pierre Geurts)
Mode of delivery (face-to-face ; distance-learning)
Recommended or required readings
Partial course notes (including exercise sets) will be made available through eCampus.
Bibliography - Norris, James R. (1998). Markov chains. Cambridge University Press. - Ross, Sheldon (2006). Introduction to probability models. Academic Press.
Assessment methods and criteria
The final grade will be a weighted average of two grades :
- that obtained after a written exam held in June (concerning both theory and exercises);
- the grade obtained after evaluation of a project.
Email : Celine.Esser@uliege.be
Department of Mathematics, Allée de la Découverte, 12, B37, 4000 Liège Belgium Office 0/62