2020/09/28 by Horatio Boedihardjo, Boedihardjo, Horatio, Xi Geng +1 · 3 citations
Engineering · Mathematics · Economics, Econometrics and Finance · #Stability and Controllability of Differential Equations #Mathematical Dynamics and Fractals #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2009.13084
We provide an account for the existence and uniqueness of solutions to rough differential equations under the framework of controlled rough paths. The case when the driving path is β-Hölder continuous, for β>1/3, is widely available in the literature. In its extension to the case when β\leqslant1/3, a main challenge and missing ingredient is to show that controlled roughs paths are closed under composition with Lipschitz transformations. Establishing such a property precisely, which has a strong algebraic nature, is a main purpose of the present article.