Erratum: Moderate Deviations Principle and Central Limit Theorem for Stochastic Cahn-Hilliard Equation in Hölder Norm

Abstract

We consider a stochastic Cahn-Hilliard partial differential equation driven by a space-time white noise. In this paper, we prove a Central Limit Theorem (CLT) and a Moderate Deviation Principle (MDP) for a perturbed stochastic Cahn-Hilliard equation in Holder norm. The techniques are based on Freidlin-Wentzell’s Large Deviations Principle. The exponential estimates in the space of  Holder continuous functions and the Garsia-Rodemich-Rumsey’s lemma plays an important role, an approach than the Li.R.  and Wang.X. Finally, we establish the CLT and MDP for stochastic Cahn-Hilliard equations with uniformly Lipschitzian coefficients.

Erratum: Moderate Deviations Principle and Central Limit Theorem for Stochastic Cahn-Hilliard Equation in Hölder Norm, published in the International Journal of Applied and Mathematical Sciences (IJAMS), Volume 1 No 1, pages 34–52, on May 05, 2024.

Erratum Details: The error pertains to equation (3.2) in the section "PROOF OF MAIN RESULTS." Specifically:

• Regarding equation (3.1), we first fix t, and in this case, it works as intended.
• However, for equation (3.2), when fixing y, in the last inequality, it is necessary to replace ∣x−y∣ with ∣t−s∣ as a correction.

MSC: 60H15, 60F05, 35B40, 35Q62

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