发表机构
Southern University of Science and Technology; Peking University（南方科技大学; 北京大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究具有赫尔德连续系数的退化随机微分方程的路径唯一性问题，利用马利瓦因紧致性准则构造强解，通过对偶山田-渡边论证及弱唯一性得出路径唯一性。
AI 中文摘要
本文研究一类由循环催化超马尔可夫链产生的、具有赫尔德连续扩散系数的退化随机微分方程的路径唯一性问题。关键步骤是利用马利瓦因紧致性准则直接构造强解，然后通过对偶的山田-渡边论证以及文献中已有的弱唯一性得到路径唯一性。
英文摘要
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.
