Abstract
The theory of regularity structures enables the definition of the following parabolic Anderson model in a very rough environment: ∂tut(x)=12Δut(x)+ut(x)W˙t(x), for t∈R+ and x∈Rd, where W˙t(x) is a Gaussian noise whose space time covariance function is singular. In this rough context we shall give some information about the moments of ut(x) when the stochastic heat equation is interpreted in the Skorohod as well as the Stratonovich sense. Of special interest is the critical case, for which one observes a blowup of moments for large times.
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