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

Nils Berglund and Christian Kuehn
Electronic J. Probability 24 (113):1-22 (2019)

Lemma 4.8 in the article [Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions] 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.

Mathematical Subject Classification: 60H15, 35K57 (primary), 81S20, 82C28 (secondary).

Keywords and phrases: Stochastic partial differential equations, parabolic equations, reaction-diffusion equations, FitzHugh-Nagumo equation, regularity structures, renormalisation.

 

Journal Homepage Published article: 10.1214/19-EJP359 MR4017131 Zbl07142907

PDF file (292 Kb) hal-01788021 arXiv/1805.02890