A note on the Malliavin–Sobolev spaces

A note on the Malliavin–Sobolev spaces

In this paper, we provide a strong formulation of the stochastic Gâteaux differentiability in order to study the sharpness of a new characterization, introduced in Mastrolia et al. (2014), of the Malliavin–Sobolev spaces. We also give a new internal structure of these spaces in the sense of sets inc...

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Veröffentlicht in:Statistics & probability letters 2016-02, Vol.109, p.45-53
Hauptverfasser: Imkeller, Peter, Mastrolia, Thibaut, Possamaï, Dylan, Réveillac, Anthony
Format: Artikel
Sprache:eng
Schlagworte:
Functional analysis
Malliavin calculus
Mathematics
Probability
Stochastic Gâteaux differentiability
Wiener space
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Zusammenfassung:In this paper, we provide a strong formulation of the stochastic Gâteaux differentiability in order to study the sharpness of a new characterization, introduced in Mastrolia et al. (2014), of the Malliavin–Sobolev spaces. We also give a new internal structure of these spaces in the sense of sets inclusion.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2015.08.020