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PreprintCC BY-SA 4.0arXiv

Pathwise uniqueness for degenerate stochastic differential equations with Hölder continuous coefficients

  • Jie Xiong
  • Wen Xu
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Abstract

We study pathwise uniqueness for cyclic catalytic stochastic differential equations whose state-dependent square-root diffusion coefficients are non-Lipschitz and degenerate on the boundary. The approach is the direct construction of a strong solution using a Malliavin compactness criterion. The key is the development of a new family of boundary-sensitive weighted Malliavin estimates for the tangent processes of the smooth approximations. Pathwise uniqueness then follows from the dual Yamada-Watanabe argument together with the weak uniqueness available in the literature.

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Cite

BibTeXRIS
BibTeX
@misc{xiong2026pathwise,
  title = {{Pathwise uniqueness for degenerate stochastic differential equations with Hölder continuous coefficients}},
  author = {Jie Xiong and Wen Xu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.22220},
  eprint = {2607.22220},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.22220},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - Pathwise uniqueness for degenerate stochastic differential equations with Hölder continuous coefficients
AU  - Jie Xiong
AU  - Wen Xu
PY  - 2026
DA  - 2026/09/06
PB  - arXiv
DO  - 10.48550/arxiv.2607.22220
UR  - https://arxiv.org/abs/2607.22220
AB  - We study pathwise uniqueness for cyclic catalytic stochastic differential equations whose state-dependent square-root diffusion coefficients are non-Lipschitz and degenerate on the boundary. The approach is the direct construction of a strong solution using a Malliavin compactness criterion. The key is the development of a new family of boundary-sensitive weighted Malliavin estimates for the tangent processes of the smooth approximations. Pathwise uniqueness then follows from the dual Yamada-Watanabe argument together with the weak uniqueness available in the literature.
ER  -