Descriptif
The goal of this course is to present the two main modern tools in probability and essential objects from a theoretical perspective as well as in applications: martingales and Markov chains. Both pertain to the theory of stochastic processes in discrete time, namely sequences of random variables which are not independent, but rather in which the law at a given time depends on the past.
Martingale theory constitutes a fantastic tool that for example allows to describe the law of the time and position of the first entry of such a process in a given subset as well as to establish almost sure convergence as time tends to infinity.
Markov chains appear very naturally in the modelisation of various phenomena for it describes the evolution of a stochastic process in which at a given time, the law of the next position in fact only depends on the present position and not the whole past trajectory.
Diplôme(s) concerné(s)
Pour les étudiants du diplôme M1 APPMS - Mathématiques Appliquées et Statistiques
This course is meant to be a second course on probability theory. Familiarity with basic measure theory and probability such as random variables, their law and
expectation, independence, Lp spaces, different notion of convergences, Law of Large Numbers & Central Limit Theorem will be assumed.
Some familiarity with Python for numerical applications can be useful.
Format des notes
Numérique sur 20Littérale/grade réduitPour les étudiants du diplôme M1 APPMS - Mathématiques Appliquées et Statistiques
Vos modalités d'acquisition :
Two written exams will take place a midterm exam (M) and a final one (F). The grade is then calculated as max(F, (M+F)/2).
L'UE est acquise si note finale transposée >= C- Crédits ECTS acquis : 6 ECTS
La note obtenue rentre dans le calcul de votre GPA.
