论文标题
固定的梯形随机过程和字段的随机限制定理
Randomized limit theorems for stationary ergodic random processes and fields
论文作者
论文摘要
我们考虑通过使用有限数量的观测值构建的“随机”统计数据，一个随机选择点的随机字段。 We generalize the invariance principle (the functional CLT), the Glivenko--Cantelli theorem, the theorem about convergence to the Brownian bridge and the Kolmogorov theorem about the limit distribution of the empirical distribution function, as well as an improved version of the CLT in A. Tempelman, Randomized multivariate central limit theorems for ergodic homogeneous random fields, Stochastic Processes and their申请。 143（2022），89-105。提到的工作中引入的随机方法允许将这些定理扩展到$ \ z^m $和$ \ r^m的所有ergodic同质随机字段。
We consider "randomized" statistics constructed by using a finite number of observations a random field at randomly chosen points. We generalize the invariance principle (the functional CLT), the Glivenko--Cantelli theorem, the theorem about convergence to the Brownian bridge and the Kolmogorov theorem about the limit distribution of the empirical distribution function, as well as an improved version of the CLT in A. Tempelman, Randomized multivariate central limit theorems for ergodic homogeneous random fields, Stochastic Processes and their Applications. 143 (2022), 89-105. The randomized approach, introduced in the mentioned work, allows to extend these theorems to all ergodic homogeneous random fields on $\Z^m$ and $\R^m.$
