The theory of rough paths via one-forms and the extension of an argument of Schwartz to rough differential equations

Abstract

We give an overview of the recent approach to the integration of rough paths that reduces the problem to classical Young integration. As an application, we extend an argument of Schwartz to rough differential equations, and prove the existence, uniqueness and continuity of the solution, which is applicable when the driving path takes values in nilpotent Lie group or Butcher group.

16 pages, To appear in Journal of the Mathematical Society of Japan, special issue dedicated to Prof. Kiyosi Itô