Electronic Journal of Probability

Corrigendum to “Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions”

Abstract

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.

Article information

Source
Electron. J. Probab., Volume 24 (2019), paper no. 113, 22 pp.

Dates
Accepted: 8 September 2019
First available in Project Euclid: 10 October 2019

https://projecteuclid.org/euclid.ejp/1570672858

Digital Object Identifier
doi:10.1214/19-EJP359

Mathematical Reviews number (MathSciNet)
MR4017131

Zentralblatt MATH identifier
07142907

Citation

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

References

• [1] N. Berglund and C. Kuehn. Regularity structures and renormalisation of FitzHugh–Nagumo SPDEs in three space dimensions. Electron. J. Probab., 21:1–48, 2016.
• [2] M. Hairer. A theory of regularity structures. Invent. Math., 198(2):269–504, 2014.