Triviality of the 2D stochastic Allen-Cahn equation

Martin Hairer, Marc D. Ryser, Hendrik Weber

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)

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.

Original languageEnglish
Article number39
Number of pages14
JournalElectronic Journal of Probability
Volume17
DOIs
Publication statusPublished - 9 Jul 2012

Keywords

  • Allen-Cahn equation
  • SPDEs
  • Stochastic quantisation
  • White noise

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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