Pathwise uniqueness for degenerate stochastic differential equations with Hölder continuous coefficients

2026/07/24 by Jie Xiong, Wen Xu
#math.PR

paper · pdf

Abstract

In this paper, we study the pathwise uniqueness problem for a class of degenerate stochastic differential equations with Hölder 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.

Related

• Pathwise uniqueness for stochastic heat equations with Hölder continuous coefficients: the white noise case
• On the pathwise uniqueness for a class of degenerate Itô-stochastic differential equations
• Pathwise uniqueness for stochastic reaction-diffusion equations in Banach spaces with an Hölder drift component
• Pathwise uniqueness for a SPDE with Hölder continuous coefficient driven by α-stable noise
• Pathwise uniqueness of one-dimensional SDEs driven by one-sided stable processes