English

Pathwise uniqueness for degenerate stochastic differential equations with H\"older continuous coefficients

Probability 2026-07-24 v1

Abstract

In this paper, we study the pathwise uniqueness problem for a class of degenerate stochastic differential equations with H\"{o}lder continuous diffusion coefficients arising from a cyclic catalytic super-Markov chain. The key step is a direct construction of a strong solution using Malliavin's compactness criteria. The pathwise uniqueness is then obtained by the dual Yamada-Watanabe argument together with the weak uniqueness already existing in the literature.

Cite

@article{arxiv.2607.22220,
  title  = {Pathwise uniqueness for degenerate stochastic differential equations with H\"older continuous coefficients},
  author = {Jie Xiong and Wen Xu},
  journal= {arXiv preprint arXiv:2607.22220},
  year   = {2026}
}