Singular perturbations to semilinear stochastic heat equations
Hairer, Martin. (2012) Singular perturbations to semilinear stochastic heat equations. Probability Theory and Related Fields, Vol. 152 (No. 1-2). pp. 265-297. ISSN 0178-8051Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/s00440-010-0322-7
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|
|Divisions:||Faculty of Science > Mathematics|
|Journal or Publication Title:||Probability Theory and Related Fields|
|Page Range:||pp. 265-297|
|Access rights to Published version:||Restricted or Subscription Access|
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