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Towards abstract Wiener model spaces

Gideon Chiusole & Peter K. Friz

Probability Theory and Related Fields2026https://doi.org/10.1007/s00440-026-01464-2article
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Abstract

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 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.

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https://doi.org/https://doi.org/10.1007/s00440-026-01464-2

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@article{gideon2026,
  title        = {{Towards abstract Wiener model spaces}},
  author       = {Gideon Chiusole & Peter K. Friz},
  journal      = {Probability Theory and Related Fields},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1007/s00440-026-01464-2},
}

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0.50

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.50 × 0.4 = 0.20
M · momentum0.50 × 0.15 = 0.07
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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