Translator Disclaimer
2012 Triviality of the 2D stochastic Allen-Cahn equation
Martin Hairer, Marc Ryser, Hendrik Weber
Author Affiliations +
Electron. J. Probab. 17: 1-14 (2012). DOI: 10.1214/EJP.v17-1731

Abstract

We consider the stochastic Allen-Cahn equation driven by mollified space-time white noise. We show that, as the mollifier is removed, the solutions converge weakly to 0, independently of the initial condition. If the intensity of the noise simultaneously converges to 0 at a sufficiently fast rate, then the solutions converge to those of the deterministic equation. At the critical rate, the limiting solution is still deterministic, but it exhibits an additional damping term.

Citation

Download Citation

Martin Hairer. Marc Ryser. Hendrik Weber. "Triviality of the 2D stochastic Allen-Cahn equation." Electron. J. Probab. 17 1 - 14, 2012. https://doi.org/10.1214/EJP.v17-1731

Information

Accepted: 30 May 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1245.60063
MathSciNet: MR2928722
Digital Object Identifier: 10.1214/EJP.v17-1731

Subjects:
Primary: 60H15
Secondary: 81T08

JOURNAL ARTICLE
14 PAGES


SHARE
Vol.17 • 2012
Back to Top