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Pré-Publication, Document De Travail Année : 2018

Erratum for " Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions "

Nils Berglund
Christian Kuehn
  • Fonction : Auteur

Résumé

Lemma 4.8 in the article [Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions, Electronic J. Probability 21 (18):1-48 (2016), hal-01141380] contains a mistake, which implies a weaker regularity estimate than the one stated in Proposition 4.11. This does not affect the proof of Theorem 2.1, but Theorems 2.2 and 2.3 only follow from the given proof if either the space dimension d is equal to 2, or the nonlinearity F (U, V) is linear in V. To fix this problem and provide a proof of Theorems 2.2 and 2.3 valid in full generality, we consider an alternative formulation of the fixed-point problem, involving a modified integration operator with nonlocal singularity and a slightly different regularity structure. We provide the multilevel Schauder estimates and renormalisation-group analysis required for the fixed-point argument in this new setting.
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Dates et versions

hal-01788021 , version 1 (08-05-2018)
hal-01788021 , version 2 (30-07-2019)

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  • HAL Id : hal-01788021 , version 1

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Nils Berglund, Christian Kuehn. Erratum for " Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions ". 2018. ⟨hal-01788021v1⟩
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