Towards Abstract Wiener Model Spaces

Abstract: Wiener spaces are in many ways the decisive setting for fundamental results on Gaussian measures: large deviations (Schilder), quasi-invariance (Cameron-Martin), differential calculus (Malliavin), support description (Stroock-Varadhan), concentration of measure (Fernique), ... Analogues of these classical results have been derived in the "enhanced" context of Gaussian rough paths and, more recently, regularity structures equipped with Gaussian models. The aim of this article is to propose a notion of "abstract Wiener model space" that encompasses the aforementioned. More specifically, we focus here on enhanced Schilder type results, Cameron-Martin shifts and Fernique estimates, offering a somewhat unified view on results in Friz-Victoir 2007 and Hairer-Weber 2015.