arXiv Open Access 2023

Towards Abstract Wiener Model Spaces

Gideon Chiusole Peter K. Friz

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Abstrak

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.

Topik & Kata Kunci

math.PR

Penulis (2)

Gideon Chiusole

Peter K. Friz

Format Sitasi

APA MLA BibTeX

Chiusole, G., Friz, P.K. (2023). Towards Abstract Wiener Model Spaces. https://arxiv.org/abs/2401.00169

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Informasi Jurnal

Tahun Terbit: 2023
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓