Introduction to the theory of discrete-time martingales including, in particular, the convergence and stopping time theorems. Application to branching processes. Introduction to Brownian motion and st
In this course, various aspects of probability theory are considered. The first part is devoted to the main theorems in the field (law of large numbers, central limit theorem, concentration inequaliti
This course gives an introduction to probability theory and stochastic calculus in discrete and continuous time. The fundamental notions and techniques introduced in this course have many applicatio
Introduction to the mathematical theory of stochastic calculus: construction of stochastic Ito integral, proof of Ito formula, introduction to stochastic differential equations, Girsanov theorem and F
L'objectif de ce cours est la maitrise des outils des processus stochastiques utiles pour un ingénieur travaillant dans les domaines des systèmes de communication, de la science des données et de l'i
The two main topics covered by this course are classical molecular dynamics and the Monte Carlo method.
Noise and fluctuations play a crucial role in science and technology. This course treats stochastic methods, applying them to both classical problems and quantum systems. It emphasizes the frameworks
This course focuses on dynamic models of random phenomena, and in particular, the most popular classes of such models: Markov chains and Markov decision processes. We will also study applications in q
This course offers an introduction to topics in stochastic analysis, oriented about theory of multi-scale stochastic dynamics. We shall learn the fundamental ideas, relevant techniques, and in general
The aim of the course is to apply the theory of martingales in the context of mathematical finance. The course provides a detailed study of the mathematical ideas that are used in modern financial mat
