Randomized limit theorems for stationary ergodic random processes and fields

Youri Davydov; Arkady Tempelman

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arXiv · 2201.08981

Randomized limit theorems for stationary ergodic random processes and fields

Youri Davydov·Arkady Tempelman

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Abstract

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 $\R^m.$

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Youri Davydov, Arkady Tempelman. 2022-01-22. Randomized limit theorems for stationary ergodic random processes and fields. https://arxiv.org/abs/2201.08981

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