Randomness plays a decisive role in a variety of contexts, and it is often necessary to take it into account in many aspects of the engineering sciences, we can name telecommunications, pattern recognition or network administration.
More generally, randomness is also a factor in economics (risk management), medicine (epidemic propagation), biology (population evolution) and statistical physics (phase transition theory).
In applications, data observed over time are often modeled by correlated random variables whose behavior we would like to predict. The aim of this course is to formalize these notions by studying two types of random processes that are fundamental to probability theory: Markov chains and martingales. Various applications will be presented to illustrate these concepts.
Bibliographical reference
"Promenade aléatoire: chaînes de Markhov et martingales", Thierry Bodineau (2023)
Level required: Good knowledge of core course MAP361.
Evaluation methods : A grading test at the end of the course.
- Teaching coordinator: Castellano Margherita
- Teaching coordinator: Djete Mao Fabrice
- Teaching coordinator: Ehrlacher Virginie
- Teaching coordinator: Guillin Arnaud
- Teaching coordinator: Guyader Arnaud
- Teaching coordinator: Jeddi Anouar
- Teaching coordinator: Leble Thomas
- Teaching coordinator: Lelievre Tony
- Teaching coordinator: Marivain Maxime
- Teaching coordinator: Marzouk Cyril
- Teaching coordinator: Monmarche Pierre
- Teaching coordinator: Ocello Antonio
- Teaching coordinator: Reygner Julien
- Teaching coordinator: Singh Arvind
- Teaching coordinator: Tardy Yoan