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Singular perturbations to semilinear stochastic heat equations
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  • Published: 06 October 2010

Singular perturbations to semilinear stochastic heat equations

  • Martin Hairer1 

Probability Theory and Related Fields volume 152, pages 265–297 (2012)Cite this article

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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.

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Authors and Affiliations

  1. Mathematics Department, The University of Warwick, Coventry, CV4 7AL, UK

    Martin Hairer

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  1. Martin Hairer
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Correspondence to Martin Hairer.

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Hairer, M. Singular perturbations to semilinear stochastic heat equations. Probab. Theory Relat. Fields 152, 265–297 (2012). https://doi.org/10.1007/s00440-010-0322-7

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  • Received: 19 February 2010

  • Revised: 01 September 2010

  • Published: 06 October 2010

  • Issue Date: February 2012

  • DOI: https://doi.org/10.1007/s00440-010-0322-7

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Mathematics Subject Classification (2000)

  • Primary 60H15
  • Secondary 60H30
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