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Singular perturbations to semilinear stochastic heat equations
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Hairer, Martin (2012) Singular perturbations to semilinear stochastic heat equations. Probability Theory and Related Fields, Vol. 152 (No. 1-2). pp. 265-297. doi:10.1007/s00440-010-0322-7 ISSN 0178-8051.
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Official URL: http://dx.doi.org/10.1007/s00440-010-0322-7
Abstract
We consider a class of singular perturbations to the stochastic heat equation or semilinear variations thereof. The interesting feature of these perturbations is that, as the small parameter ε tends to zero, their solutions converge to the ‘wrong’ limit, i.e. they do not converge to the solution obtained by simply setting ε = 0. A similar effect is also observed for some (formally) small stochastic perturbations of a deterministic semilinear parabolic PDE. Our proofs are based on a detailed analysis of the spatially rough component of the equations, combined with a judicious use of Gaussian concentration inequalities.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Probability Theory and Related Fields | ||||
Publisher: | Springer | ||||
ISSN: | 0178-8051 | ||||
Official Date: | 2012 | ||||
Dates: |
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Volume: | Vol. 152 | ||||
Number: | No. 1-2 | ||||
Page Range: | pp. 265-297 | ||||
DOI: | 10.1007/s00440-010-0322-7 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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