Open Access
2019 Corrigendum to “Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions”
Nils Berglund, Christian Kuehn
Electron. J. Probab. 24: 1-22 (2019). DOI: 10.1214/19-EJP359


Lemma 4.8 in the article [1] 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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Nils Berglund. Christian Kuehn. "Corrigendum to “Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions”." Electron. J. Probab. 24 1 - 22, 2019.


Received: 3 June 2018; Accepted: 8 September 2019; Published: 2019
First available in Project Euclid: 10 October 2019

zbMATH: 07142907
MathSciNet: MR4017131
Digital Object Identifier: 10.1214/19-EJP359

Primary: 35K57 , 60H15
Secondary: 81S20 , 82C28

Keywords: FitzHugh–Nagumo equation , Parabolic equations , reaction–diffusion equations , Regularity structures , renormalisation , Stochastic partial differential equations

Vol.24 • 2019
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