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


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.


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Martin Hairer. Marc Ryser. Hendrik Weber. "Triviality of the 2D stochastic Allen-Cahn equation." Electron. J. Probab. 17 1 - 14, 2012.


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

Primary: 60H15
Secondary: 81T08

Keywords: Allen-Cahn equation , SPDEs , Stochastic quantisation , White noise

Vol.17 • 2012
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