From probability to PDEs : Stochastic differential equations and applications

Abstract

The goal of this project is to give probabilistic representations of solution of different types of PDEs. In particular, we study the Brownian motion and relate this concept with the solution of linear PDEs. Moreover, we study the fractional Laplacian starting from long jump random walks. Finally, we give a probabilistic solution of nonlinear PDEs thanks to the Brownian snake and relate this type of PDE with the singular Yamabe problem.