Work

Pathwise uniqueness for degenerate stochastic differential equations with Hölder continuous coefficients

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2607.22220

Authors: Xiong, Jie, Xu, Wen

Institutions: Southern University of Science and Technology, Peking University

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Awards: G1351101462, G259192822, G8700735110

OpenAlex ID: W7171360854

Cites: 1

Cited by: 1

Related to: 10