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Triviality of the 2D stochastic Allen-Cahn equation
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Hairer, Martin, Ryser, Marc D. and Weber, Hendrik (2012) Triviality of the 2D stochastic Allen-Cahn equation. Electronic Journal of Probability, Vol.17 . pp. 1-14. doi:10.1214/EJP.v17-1731
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Official URL: http://dx.doi.org/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.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Stochastic analysis | ||||
| Journal or Publication Title: | Electronic Journal of Probability | ||||
| Publisher: | Institute of Mathematical Statistics | ||||
| ISSN: | 1083-6489 | ||||
| Official Date: | 2012 | ||||
| Dates: |
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| Volume: | Vol.17 | ||||
| Page Range: | pp. 1-14 | ||||
| DOI: | 10.1214/EJP.v17-1731 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Open Access | ||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC), Royal Society (Great Britain), Leverhulme Trust (LT), Hydro-Québec | ||||
| Grant number: | EP/D071593/1 (EPSRC) |
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