Second semester
Martingales and Levy Process
Objectives
Know and apply basic techniques using martingale-type tools. Master the notions of stopping time and martingale hooks.
Some notions of continuous-time processes: Brownian motion, Poisson processes, compound Poisson processes.
Course outline
Stochastic processes, filtering, stopping times
Sub-martingales and over-martingales in discrete time
Stopping and convergence theorems
Continuous-time processes, Poisson processes, Brownian motion
Prerequisites
Measurement theory, general probability