We construct a scale of non-Gaussian measures supported on Sobolev spaces on the 3D torus using a new technique due to Barashkov & Gubinelli. These measures were first introduced and constructed in 2D by Oh & Tzvetkov in the study of quasi-invariance of a scale of Gaussian measures under the transport of the defocusing, cubic, nonlinear Klein-Gordon equation. They provide an interesting and simple class of measures for which Wick renormalisation suffices to construct the measures but the classical Nelson construction fails.查看全文