Multi-indices coproducts from ODEs to singular SPDEs

Fuente: arXiv
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Autori principali: Bruned, Yvain, Hou, Yingtong
Natura: Preprint
Pubblicazione: 2024
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author Bruned, Yvain
Hou, Yingtong
author_facet Bruned, Yvain
Hou, Yingtong
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2405_11314
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Multi-indices coproducts from ODEs to singular SPDEs
Bruned, Yvain
Hou, Yingtong
Probability
Numerical Analysis
Analysis of PDEs
Rings and Algebras
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.
title Multi-indices coproducts from ODEs to singular SPDEs
topic Probability
Numerical Analysis
Analysis of PDEs
Rings and Algebras
url https://arxiv.org/abs/2405.11314