2023/12/30 by Gideon Chiusole, Chiusole, Gideon, Peter K. Friz +1
Computer Science · Mathematics · #28C20 #46G12 #60B11 #60L20 #60L30 #FOS: Mathematics #Morphological variations and asymmetry #Probability (math.PR) #Topological and Geometric Data Analysis #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2401.00169
openalex publication_date 2023/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
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), etc. 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 similar notion directly on this enhanced level - an 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 of Friz--Victoir and Hairer--Weber.