Solving rough differential equations with the theory of the regularity structures
Abstract
The theory of the rough paths allows to give a meaning to the differential equations dYt = F(Yt)dXt; where X is [infinity]-Hölder with [alpha is an element of] (0; 1] and to prove the existence and the unicity of a solution. Here we propose to approach this equation with the theory of the regularity structures and to find the results already known with this framework.