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Boundedness of the Density of Wiener Functionals with Low Regularity

  • Hua Zhang
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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.

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026boundedness,
  title = {{Boundedness of the Density of Wiener Functionals with Low Regularity}},
  author = {Hua Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33578},
  eprint = {2610.33578},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33578},
}
RIS
TY  - UNPB
TI  - Boundedness of the Density of Wiener Functionals with Low Regularity
AU  - Hua Zhang
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2610.33578
UR  - https://arxiv.org/abs/2610.33578
AB  - 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.
ER  -