Randomized limit theorems for stationary ergodic random processes and fields

Youri Davydov and Arkady Tempelman

Stochastic Processes and their Applications, 2024, vol. 174, issue C

Abstract: Using the randomization approach, introduced by A. Tempelman in Randomized multivariate central limit theorems for ergodic homogeneous random fields, Stochastic Processes and their Applications. 143 (2022), 89–105, we prove: (a) a randomized version of the invariance principle (the functional CLT); (b) a version the Glivenko–Cantelli theorem; (c) a randomized theorem about convergence of empirical processes to the Brownian bridge. We also weaken the moment condition in the randomized CLTs, proved in the mentioned article. The main point of our work is that most of our theorems are valid for all ergodic homogeneous random fields on Zm and Rm,m≥1.

Keywords: Central limit theorem; Stationary random process; Homogeneous random fields; Invariance principle; Glivenko–Cantelli theorem; Brownian bridge; Empirical processes; Randomization (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104380

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