Probability theory and introduction to stochastic processes

The course will be given in English if necessary. It is a mathematical advanced course which is strongly recommended to students who want to proceed in Mathematics in France or abroad. In the following of teh cours of S7 we introduced in a rigourous way neaw notions such as characteristic function, Gaussian processes, Law of 0-1, Borel-Cantelli lemma. NEw modelisation tools such as conditionnal expectation and martingales, are studied.

Prerequisite : One of the two course S07_MTH_A_1FH Outils mathématiques avancés pour les probabilités et l’apprentissage statistique ou S07_MTH_A_3EG Outils mathématiques avancés pour l’analyse des équations aux dérivées partielles or any equivalent course

Characteristic functions Gaussian processes Random sequences, limit theorems Conditional expectation, martingales and stopping time