A note on the Malliavin-Sobolev spaces
Peter Imkeller, Thibaut Mastrolia (CEREMADE), Dylan Possama\"i, (CEREMADE), Anthony R\'eveillac (INSA Toulouse, IMT)

TL;DR
This paper refines the understanding of Malliavin-Sobolev spaces by providing a strong formulation of stochastic Gâteaux differentiability and analyzing their internal set-inclusion structure.
Contribution
It introduces a strong formulation of stochastic Gâteaux differentiability and offers a new internal structure characterization of Malliavin-Sobolev spaces.
Findings
Established a strong formulation of stochastic Gâteaux differentiability.
Provided a new characterization of the internal structure of Malliavin-Sobolev spaces.
Analyzed the sharpness of a recent characterization of these spaces.
Abstract
In this paper, we provide a strong formulation of the stochastic G{\^a}teaux differentiability in order to study the sharpness of a new characterization, introduced in [6], of the Malliavin-Sobolev spaces. We also give a new internal structure of these spaces in the sense of sets inclusion.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Numerical methods in inverse problems
