Stochastic calculus and optimization

  • Stochastic calculus: The objective of this course is to study a certain class of continuous-time random processes. It starts with a detailed study of Brownian motion which is the basic tool of stochastic calculus. Then, the notion of stochastic integral is introduced. One of the goals of this course is to study the notion of stochastic differential equation which is used in many applications.
  • Optimization: Gradient descent, Block gradient descent, Stochastic gradient descent, Acceleration (link with ODEs, Nesterov method, Stochastic versions (ADAM, …)