One-dimensional reflected rough differential equations

We prove existence and uniqueness of the solution of a one-dimensional rough differential equation driven by a step-2 rough path and reflected at zero. The whole difficulty of the problem (at least as far as uniqueness is concerned) lies in the non-continuity of the Skorohod map with respect to the topologies under consideration in the rough case. Our argument to overcome this obstacle is inspired by some ideas we introduced in a previous work dealing with rough kinetic PDEs arXiv:1604.00437.