Corrigendum to “Regularity structures and renormalisation of Fitzhugh-Nagumo SPDEs in three space dimensions”. (English) Zbl 1427.60117

Berglund, Nils; Kuehn, Christian

Electron. J. Probab. 24, Paper No. 113, 22 p. (2019).

Summary: Lemma 4.8 in the authors’ paper [ibid. 21, Paper No. 18, 48 p. (2016; Zbl 1338.60152)] 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.

MSC:

60H15	Stochastic partial differential equations (aspects of stochastic analysis)
35R60	PDEs with randomness, stochastic partial differential equations
35K57	Reaction-diffusion equations
81S20	Stochastic quantization
82C28	Dynamic renormalization group methods applied to problems in time-dependent statistical mechanics

Keywords:

stochastic partial differential equations; parabolic equations; reaction-diffusion equations; FitzHugh-Nagumo equation; regularity structures; renormalisation

Citations:

Zbl 1338.60152

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.