Probability theory and introduction to stochastic processes

Lecturer(s): Marie-Christophette BLANCHET, Elisabeth MIRONESCU
Course ⋅ 16 hTC ⋅ 16 h


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 function, Gaussian processes, conditionnal expectation, stopping times, discrete time martingales


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

Learning Outcomes

  • Modelisation with discrete stochastic processes


Final Mark= 75%kowledge+25% Know How Knowledge= 80%final exam+20% continous assesment Know how= 100% continuous assesment