Composition and substitution of Regularity Structures B-series

Yvain Bruned

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arXiv · 2310.14242

Composition and substitution of Regularity Structures B-series

Yvain Bruned

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Abstract

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.

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Yvain Bruned. 2023-10-22. Composition and substitution of Regularity Structures B-series. https://arxiv.org/abs/2310.14242

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