In this work, we introduce Regularity Structures B-series which are used for describing solutions of singular stochastic partial differential equations (SPDEs). We define composition and substitutions of these B-series and as in the context of B-series for ordinary differential equations, these operations can be rewritten via products and Hopf algebras which have been used for building up renormalised models. These models provide a suitable topology for solving singular SPDEs. This new construction sheds a new light on these products and open interesting perspectives for the study of singular SPDEs in connection with B-series.

翻译：本文引入用于描述奇异随机偏微分方程解的正则结构B-级数。我们定义了这类B-级数的复合运算与代换运算，与常微分方程B-级数理论类似，这些运算可通过乘积与Hopf代数重新表述——该代数体系正是构建重整化模型的核心工具。此类模型为求解奇异随机偏微分方程提供了适定的拓扑框架。新构造方法为理解这些代数乘积结构提供了全新视角，并为结合B-级数理论研究奇异随机偏微分方程开辟了新的前景。