论文标题
通过流量近似构建一般粗糙的微分方程
Constructing general rough differential equations through flow approximations
论文作者
论文摘要
非线性缝纫引理构建构造从称为几乎流量的Braod类别的粗糙微分方程的流动。我们考虑一类几乎可以通过向后误差分析的精神来通过普通微分方程的解决方案来近似的流量。在扩展分析中，混合代数和分析是带有剩余和组成公式的泰勒公式。在要集成的非平滑矢量场上的合适代数结构，我们在一个框架中恢复了有关各种驾驶路径的高阶扩展的几个结果。我们还扩展了驾驶粗糙路径的概念。我们还介绍了一个新的分支粗糙路径系列，称为芳香的粗糙路径，以芳香的屠夫系列建模。
The non-linear sewing lemma constructs flows of rough differential equations from a braod class of approximations called almost flows. We consider a class of almost flows that could be approximated by solutions of ordinary differential equations, in the spirit of the backward error analysis. Mixing algebra and analysis, a Taylor formula with remainder and a composition formula are central in the expansion analysis. With a suitable algebraic structure on the non-smooth vector fields to be integrated, we recover in a single framework several results regarding high-order expansions for various kind of driving paths. We also extend the notion of driving rough path. We also introduce as an example a new family of branched rough paths, called aromatic rough paths modeled after aromatic Butcher series.
