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Probability Theory and Related Fields

, Volume 152, Issue 1–2, pp 265–297 | Cite as

Singular perturbations to semilinear stochastic heat equations

  • Martin Hairer
Article

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.

Mathematics Subject Classification (2000)

Primary 60H15 Secondary 60H30 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Mathematics DepartmentThe University of WarwickCoventryUK

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