Multi-indices coproducts from ODEs to singular SPDEs

Bruned, Yvain; Hou, Yingtong

doi:10.1090/tran/9411

Multi-indices coproducts from ODEs to singular SPDEs
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by Yvain Bruned and Yingtong Hou;

Trans. Amer. Math. Soc. 378 (2025), 4903-4928

DOI: https://doi.org/10.1090/tran/9411

Published electronically: March 4, 2025

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Abstract:

In this work, we introduce explicit formulae for the coproducts at play for multi-indices in ODEs and in singular SPDEs. The two coproducts described correspond to versions of the Butcher-Connes-Kreimer and extraction-contraction coproducts with multi-indices. The main idea is to use the fact that the coproducts are the adjoint of dual products for which one has an explicit simple formula. We are able to derive the explicit formulae via an inner product defined from a symmetry factor easily computable for multi-indices.

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Multi-indices coproducts from ODEs to singular SPDEs
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Abstract: