发表机构
King’s College London; Kuwait University（伦敦国王学院; 科威特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为流形值马尔可夫链建立样本Fréchet均值的中心极限定理，将独立情形的渐近理论推广至相依过程，并给出基于曲率界和Wasserstein混合条件的充分条件，应用于压缩随机映射系统。
AI 中文摘要
本文建立了取值于流形的平稳遍历马尔可夫链的样本Fréchet均值的中心极限定理，将先前针对独立观测建立的渐近理论推广到一类相依的流形值过程。我们的结果在适当的局部正则性条件下，从总体Fréchet均值处的中心极限条件推导出样本Fréchet均值的渐近正态性。我们进一步给出了使这些假设成立的充分几何与概率条件，这些条件以曲率界和Wasserstein混合条件的形式表述。作为应用，我们为一类由压缩随机映射生成的随机动力系统建立了样本Fréchet均值的中心极限定理。
英文摘要
In this article, we establish central limit theorems for sample Fréchet means of stationary ergodic Markov chains taking values in manifolds, extending the asymptotic theory previously developed for independent observations to a class of dependent manifold-valued processes. Our results derive the asymptotic normality of the sample Fréchet mean from a central limit condition at the population Fréchet mean, under suitable local regularity conditions. We further provide sufficient geometric and probabilistic conditions under which these assumptions hold, formulated in terms of curvature bounds and a Wasserstein mixing condition. As an application, we establish a central limit theorem for sample Fréchet means for a class of random dynamical systems generated by contractive random maps.
Comments32 pages
