2017-2018 / MATH1222-3

Introduction to stochastic processes, Markov chains


20h Th, 10h Pr, 10h Mon. WS

Number of credits

 Bachelor in computer science5 crédits 
 Master in data science (120 ECTS)5 crédits 
 Master of science in computer science and engineering (120 ECTS)5 crédits 
 Bachelor in mathematics4 crédits 


Céline Esser, Pierre Geurts


Pierre Geurts

Language(s) of instruction

French language

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.


Work placement(s)

Organizational remarks


Céline Esser
Email : Celine.Esser@uliege.be 
Department of Mathematics, Allée de la Découverte, 12, B37, 4000 Liège Belgium Office 0/62