Year: 2026
Type: preprint
Abstract: In this paper we prove that if a Wiener functional $F$ is $1+δ$-differentiable in the Malliavin sense for some $δ>0$ and satisfies the nondegeneracy condition, then the density of the law of $F$ exists, is bounded and is Hölder continuous of every exponent $β<δ$. This gives a partial positive answer to a problem proposed by Watanabe [13]; to date, this seems to be the best result available for the boundedness of the density of Wiener functionals. The approach is based on the fractional order Sobolev spaces associated with a probability measure and on the Riesz transform.
Source: arXiv (Cornell University)
Author: Zhang, Hua
Institution: Jiangxi University of Finance and Economics
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
Awards: G1203918405, G176459693, G3832849291
OpenAlex ID: W7223912109