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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. ISSN 1083-6489

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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 > 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:

Date	Event
2012	Published

Volume:

Vol.17

Page Range:

pp. 1-14

Identification Number:

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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