标题： 控制粗糙路径：一个一般的霍普夫代数设置 显示英文标题

标题： Controlled rough paths: a general Hopf-algebraic setting

摘要： 我们为一类组合霍普夫代数设置了受控粗糙路径，包括乘积、Butcher-Connes-Kreimer 和 Munthe-Kaas--Wright 霍普夫代数。 我们考虑的控制类包括 Hölder 连续路径和（不一定连续）具有有界$p$-变差的路径。 我们通过在合适的受控粗糙路径巴拿赫空间中应用不动点方法，证明了这种一般情况下提升初值问题解的存在性和唯一性，并证明了一个通用极限定理，解决了解相对于参数和初始条件的鲁棒性问题。 显示英文摘要

摘要： We set up controlled rough paths for a class of combinatorial Hopf algebras, encompassing shuffle, Butcher-Connes-Kreimer and Munthe-Kaas--Wright Hopf algebras. The class of controls we consider encompasses both H\"older continuous paths and (not necessarily continuous) paths with bounded $p$-variation. We prove existence and uniqueness of the solution of a lifted initial value problem in this general setting by applying the fixed point method in a suitable Banach space of controlled rough paths, and we prove a universal limit theorem addressing the robustness of the solution with respect to the parameters and the initial condition.