Electronic Journal of Probability
- Electron. J. Probab.
- Volume 24 (2019), paper no. 113, 22 pp.
Corrigendum to “Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions”
Lemma 4.8 in the article  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.
Electron. J. Probab., Volume 24 (2019), paper no. 113, 22 pp.
Received: 3 June 2018
Accepted: 8 September 2019
First available in Project Euclid: 10 October 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60H15: Stochastic partial differential equations [See also 35R60] 35K57: Reaction-diffusion equations
Secondary: 81S20: Stochastic quantization 82C28: Dynamic renormalization group methods [See also 81T17]
Berglund, Nils; Kuehn, Christian. Corrigendum to “Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions”. Electron. J. Probab. 24 (2019), paper no. 113, 22 pp. doi:10.1214/19-EJP359. https://projecteuclid.org/euclid.ejp/1570672858
- Related item: Berglund, Nils; Kuehn, Christian. Regularity structures and renormalisation of FitzHugh–Nagumo SPDEs in three space dimensions. Electron. J. Probab. 21 (2016), paper no. 18, 48 pp. doi:10.1214/16-EJP4371.