Renormalisation from non-geometric to geometric rough paths

IF 1.5 Q2 PHYSICS, MATHEMATICAL
Y. Bruned
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引用次数: 9

Abstract

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.
从非几何到几何粗糙路径的重整化
Hairer-Kelly图用于建立几何和非几何粗糙路径之间的对应关系。最近,在(arxiv 1810.12179)中提出了一种新的粗糙路径重整化,建立在这个映射和Lyons-Victoir扩展定理的基础上。在这项工作中,我们将这种重整与现有的BPHZ和局部产品重整进行了比较。我们证明了它们在一定意义上与hair - kelly映射可交换,并在(arxiv 1810.12179)框架中给出了一个显式公式。我们还看到(arXiv:1712.01965)中从非几何粗糙路径移动到几何粗糙路径的替代方法中的重整化行为。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.30
自引率
0.00%
发文量
16
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