论文标题
从非几何变为几何粗糙路径
Renormalisation from non-geometric to geometric rough paths
论文作者
论文摘要
已经引入了Hairer-Kelly地图，以在几何和非几何粗糙路径之间建立对应关系。最近，在此地图和Lyons-Victoir扩展定理上建立的（Arxiv 1810.12179）中提出了对粗糙路径的新重量法化。在这项工作中，我们将这种重态度与现有的重态化和诸如BPHZ和当地产品重态化的现有化度进行了比较。我们证明了它们在某种意义上用毛发凯利地图上下班，并在（Arxiv 1810.12179）的框架中显示出明确的公式。我们还看到（Arxiv：1712.01965）中的替代方法中的肾小效应如何从非几何变为几何粗糙路径。
The Hairer-Kelly map has been introduced for establishing a correspondence between geometric and non-geometric rough paths. Recently, a new renormalisation on rough paths has been proposed in (arxiv 1810.12179), built on this map and the Lyons-Victoir extension theorem. In this work, we compare this renormalisation with the existing ones such as BPHZ and the local products renormalisations. We prove that they commute in a certain sense with the Hairer-Kelly map and exhibit an explicit formula in the framework of (arxiv 1810.12179). We also see how the renormalisation behaves in the alternative approach in ( arXiv:1712.01965) for moving from non-geometric to geometric rough paths.
