We discuss the relation between the statistical question of inadmissibility and the probabilistic question of transience. Brown (1971) proved the mathematical link between the admissibility of the mean of a Gaussian distribution and the recurrence of a Brownian motion, which holds for $\mathbb{R}^{2}$ but not for $\mathbb{R}^{3}$ in Euclidean space. We extend this result to symmetric, non-Gaussian distributions, without assuming the existence of moments. As an application, we prove that the relation between the inadmissibility of the predictive density of a Cauchy distribution under a uniform prior and the transience of the Cauchy process differs from dimensions $\mathbb{R}^{1}$ to $\mathbb{R}^{2}$. We also show that there exists an extreme model that is inadmissible in $\mathbb{R}^{1}$.

翻译：我们探讨了统计学中不可接受性问题与概率学中暂态性之间的关联。Brown（1971）证明了高斯分布均值的可接受性与布朗运动的常返性之间的数学联系，该结论在欧氏空间$\mathbb{R}^{2}$中成立，但在$\mathbb{R}^{3}$中不成立。我们将这一结果推广至对称非高斯分布，且不要求矩的存在性。作为应用，我们证明了在均匀先验下柯西分布预测密度的不可接受性与柯西过程的暂态性之间的关系，在$\mathbb{R}^{1}$与$\mathbb{R}^{2}$维度上存在差异。此外，我们证明了存在一种极端模型在$\mathbb{R}^{1}$中具有不可接受性。