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 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：本文引入正则结构B-级数，用于描述奇异随机偏微分方程（SPDEs）的解。我们定义了这些B-级数的复合与代换运算，与常微分方程中B-级数的情形类似，这些运算可通过乘积与Hopf代数重新表述，而后者已被用于构建重整化模型。这些模型为求解奇异SPDEs提供了合适的拓扑结构。这一新构造为这些乘积提供了新的视角，并为结合B-级数研究奇异SPDEs开启了有趣的前景。