2024-2025 / MATH1222-3

Introduction to stochastic processes

Duration

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

Number of credits

 Bachelor of Science (BSc) in Engineering5 crédits 
 Bachelor of Science (BSc) in Computer Science5 crédits 
 Master MSc. in Data Science, professional focus5 crédits 
 Master MSc. in Data Science and Engineering, professional focus5 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

The course covers the following topics:

- Markov Chains (Definition, transition matrix and graph, state classifications, asymptotic behavior, mean time to first passage or return)

- Poisson Processes

- Markov Processes

- Queuing Theory

Learning outcomes of the learning unit

After the course, students will master the main properties of most classical stochastic processes.

Prerequisite knowledge and skills

good understanding of concepts in probability theory, matrix calculus, integral calculus, and graph theory.

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 also have 10 hours of personal work (10h TD). This work will be carried out in groups, and the guidelines will be provided during the theoretical class.

Mode of delivery (face to face, distance learning, hybrid learning)

Course materials and recommended or required readings

Platform(s) used for course materials:
- eCampus


Further information:

Course notes and exercises lists are available through eCampus. 

Bibliography
- Norris, James R. (1998). Markov chains. Cambridge University Press.
- Ross, Sheldon (2006). Introduction to probability models. Academic Press.

Exam(s) in session

Any session

- In-person

written exam ( open-ended questions )

Written work / report


Further information:

The final grade will be a weighted average of two grades :

- the grade obtained during a written exam organized in the May-June session, covering theory questions and exercises (70%)

- the grade corresponding to the evaluation of the personal work carried out during the course (30%). A presentation of the project may be required.


 

Work placement(s)

Organisational remarks and main changes to the course

Contacts

Theory: C. Esser (Celine.Esser@uliege.be)

Exercises: P. Hrebenar 

Project: P. Geurts (P.Geurts@uliege.be)

Association of one or more MOOCs