2020-2021 / MATH1222-3

Introduction to stochastic processes

Duration

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

Number of credits

 Bachelor of Science (BSc) in Computer Science5 crédits 
 Bachelor in mathematics4 crédits 

Lecturer

Céline Esser, Pierre Geurts

Coordinator

Pierre Geurts

Language(s) of instruction

French language

Organisation and examination

Teaching in the second semester

Schedule

Schedule online

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, hybrid learning)

Organisational adjustments related to the current health context

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

Below you will find information on the evaluation methods planned for in-person and remote exams as well as those planned for hybrid sessions. Depending on how the health crisis evolves, the chosen method will be communicated to you no later than one month before the start of the exam session.

Any session :

- In-person

written exam ( open-ended questions )

- Remote

written exam ( open-ended questions )

- If evaluation in "hybrid"

preferred in-person


Additional information:

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

Contacts

Amir Aboubacar
Email : a.aboubacar@uliege.be 


Bât. B37 Probabilités et statistique mathématique
Quartier Polytech 1 allée de la Découverte 12
4000 Liège 1
Belgique