论文标题
分支粗糙路径的转移原理
A Transfer Principle for Branched Rough Paths
论文作者
论文摘要
一个分支的粗糙路径$ x $由$ x \ colon [0，t] \ to \ mathbb r^d $的粗糙积分组成，可能无法满足零件的集成。使用Kelly的支架扩展[KEL12]，我们通过光滑的地图定义了分支粗糙路径的推动概念，这自然导致了平滑歧管上分支粗糙路径的定义。一旦固定了协变量的衍生物，我们就能为这种粗糙路径提供一个规范，无坐标的积分定义。在根据其括号扩展方面表征了准几何粗糙路径之后，我们使用相同的框架来定义由准几何粗糙路径驱动的歧管值的粗略微分方程（RDE）。这些结果将以前的工作扩展到$ 3> p $ -ROUGH路径[ABCRF22]本身，本身是Meyer and Emery [Mey81，E89，E90]开发的ITO微积分的概括，以设置非定期较低的非几点计算。
A branched rough path $X$ consists of a rough integral calculus for $X \colon [0, T] \to \mathbb R^d$ which may fail to satisfy integration by parts. Using Kelly's bracket extension [Kel12], we define a notion of pushforward of branched rough paths through smooth maps, which leads naturally to a definition of branched rough path on a smooth manifold. Once a covariant derivative is fixed, we are able to give a canonical, coordinate-free definition of integral against such rough paths. After characterising quasi-geometric rough paths in terms of their bracket extension, we use the same framework to define manifold-valued rough differential equations (RDEs) driven by quasi-geometric rough paths. These results extend previous work on $3 > p$-rough paths [ABCRF22], itself a generalisation of the Ito calculus on manifolds developed by Meyer and Emery [Mey81, E89, E90], to the setting of non-geometric rough calculus of arbitrarily low regularity.
