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

Jie Xiong; Wen Xu

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arXiv · 2607.22220

Pathwise uniqueness for degenerate stochastic differential equations with H\"older 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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BibTeX RIS

Jie Xiong, Wen Xu. 2026-07-24. Pathwise uniqueness for degenerate stochastic differential equations with H\"older continuous coefficients. https://arxiv.org/abs/2607.22220

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