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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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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DOI: https://doi.org/10.1007/s00440-010-0322-7
Mathematics Subject Classification (2000)
- Primary 60H15
- Secondary 60H30