Singular perturbations to semilinear stochastic heat equations

Details Singular perturbations to semilinear stochastic heat equations Singular perturbations to semilinear stochastic heat equations

2010-02-19

arxiv.org/abs/1002.3722v3

Mathematics

Probability

To appear in PTRF

Scientific paper

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 epsilon tends to zero, their solutions converge to the 'wrong' limit, i.e. they do not converge to the solution obtained by simply setting epsilon = 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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