论文标题
Bogoliubov型递归规则性结构的重新归式递归
Bogoliubov type recursions for renormalisation in regularity structures
论文作者
论文摘要
Hairer的规律性结构改变了奇异随机部分微分方程的解决方案理论。正重新分析的概念是中心的，这两种重量化程序之间的复杂相互作用是通过串联的双鼠和代数Birkhoff型分解的组合来捕获的。这项工作通过定义类似于Connes的Bogoliubov型递归以及Kreimer的BPHZ重生化表述来重新审视后者。然后，我们将我们的方法应用于SPDE的重量化问题。
Hairer's regularity structures transformed the solution theory of singular stochastic partial differential equations. The notions of positive and negative renormalisation are central and the intricate interplay between these two renormalisation procedures is captured through the combination of cointeracting bialgebras and an algebraic Birkhoff-type decomposition of bialgebra morphisms. This work revisits the latter by defining Bogoliubov-type recursions similar to Connes and Kreimer's formulation of BPHZ renormalisation. We then apply our approach to the renormalisation problem for SPDEs.
