Multi-indices coproducts from ODEs to singular SPDEs
Probability
2026-01-27 v2 Numerical Analysis
Analysis of PDEs
Numerical Analysis
Rings and Algebras
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 these coproducts are the adjoints of dual products for which one has explicit simple formulae. We are able to derive the explicit formulae via an inner product defined from a symmetry factor easily computable for multi-indices.
Cite
@article{arxiv.2405.11314,
title = {Multi-indices coproducts from ODEs to singular SPDEs},
author = {Yvain Bruned and Yingtong Hou},
journal= {arXiv preprint arXiv:2405.11314},
year = {2026}
}
Comments
30 pages