Objectifs

The goal is to provide a solid intuitive understanding of probability and stochastic processes. The course serves as a preparation for subsequent courses of the program.

The course will be given face-to-face in the classroom. Depending on the evolution of the COVID-19 situation, adaptations of these plans may be necessary during the semester.

Contenus

Probability theory and probability calculus.

Important laws, such as the law of total probability, the rule of the iterated expectation, etc.

Moment generating functions and their applications.

Famous families of distributions.

Markov chains.

Lévy processes, in particular the Poisson process and the Wiener process.

Absolute and quadratic variation of a process

Martingales

Références

P. Olofsson and M. Andersson: Probability, Statistics and Stochastic Processes. Wiley, second edition, 2012.

S.M. Ross. Introduction to probability models. Harcourt/Academic Press, Burlington, MA, seventh edition, 2000.

Evaluation

1ère tentative

Examen:

Ecrit 3h00 heures

Documentation:

Non autorisée

Calculatrice:

Autorisée avec restrictions

Evaluation:

Session normale : écrit, 3 heures, calculatrice non-programmable autorisée (60% + two mid-term exams 40%)

En raison de l’évolution sanitaire liée au COVID-19, les plans d’études peuvent connaître des adaptations en cours de semestre.

Rattrapage

Examen:

Ecrit 3h00 heures

Documentation:

Non autorisée

Calculatrice:

Autorisée avec restrictions

Evaluation:

Écrit, 3 heures, calculatrice non-programmable autorisée (100%)

Les autres éléments restent.

En raison de l’évolution sanitaire liée au COVID-19, les plans d’études peuvent connaître des adaptations en cours de semestre.