重整化的粗糙路径观点
A Rough Path Perspective on Renormalization
摘要：
发展了粗糙路径平移的代数理论。特别注意的情况下，分支粗糙的路径，其基本的代数结构（康纳斯-Kreimer，格罗斯曼-拉森），使其成为一个有用的模型的情况下，在Hairer意义上的规则性结构。前李结构被认为是一个基本规则，允许直接理解的翻译（即重整化）方程正在考虑。这种构造对于Bruned-Hairer-Zambotti（2016）的正则性结构的代数重整化理论也是新颖的，详细讨论了与之的联系。
英文摘要：
We develop the algebraic theory of rough path translation. Particular attention is given to the case of branched rough paths, whose underlying algebraic structure (Connes-Kreimer, Grossman-Larson) makes it a useful model case of a regularity structure in the sense of Hairer. Pre-Lie structures are seen to play a fundamental rule which allow a direct understanding of the translated (i.e. renormalized) equation under consideration. This construction is also novel with regard to the algebraic renormalization theory for regularity structures due to Bruned--Hairer--Zambotti (2016), the links with which are discussed in detail.
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