Foundations of regularity structures

正则结构的基础

• 批准号: 288774704
• 负责人: Professor Dr. Peter Karl Friz
• 金额: --
• 依托单位: Institut für Mathematik
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/288774704?language=en
• 关键词: Foundations; regularity; structures

Regularity structures in the sense of Hairer (2014) can be seen as major generalization of Lyons' ough path theory, with additional ingredients from renormalization theory, and also drawing inspiration from PDE theory in Holder spaces. We will explore a new approach to renormalization questions, study the scope of non-local operators in Hairer's theory, as well as the role of Malliavin calculus in (Gaussian) models on suitable regularity structures.

Hairer（2014）意义上的正则性结构可以被看作是里昂的ough路径理论的主要推广，具有来自重整化理论的额外成分，并且还从保持器空间中的PDE理论中汲取灵感。我们将探索重整化问题的新方法，研究Hairer理论中非局部算子的范围，以及Malliavin演算在（高斯）模型中对适当正则结构的作用。