A review of probability theory foundations

Ects : 6

Enseignant responsable :

  • DJALIL CHAFAI

Volume horaire : 15

Description du contenu de l'enseignement :

- Random variables, expectations, laws, independence

- Inequalities and limit theorems, uniform integrability

- Conditioning, Gaussian random vectors

- Bounded variation and Lebegue-Stieltjes integral

- Stochastic processes, stopping times, martingales

- Brownian motion : martingales, trajectories, construction

- Wiener stochastic integral and Cameron-Martin formula