Construction of a Scale of Non-Gaussian Measures in 3D. (arXiv:1808.03158v1 [math.PR])
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