@inproceedings{9f3334cde19b4ce394996ab2289a6ba2,
title = "Empirical process sampled along the sums of a stationary process",
abstract = "Let (Xℓ)ℓ∈ℤd be a real random field (r. f.) indexed by ℤd with common probability distribution function F. Let (zk)∞k=0 be a sequence in ℤd. The empirical process obtained by sampling the random field along (zk) is ∑nk−=10[1Xzk≤s − F(s)]. We give conditions on (zk) that imply the Glivenko–Cantelli theorem for the empirical process sampled along (zk) in different cases (independent, associated or weakly correlated random variables). We consider also the functional central limit theorem when the Xℓ are i. i. d. These conditions are examined when (zk) is provided by the sums of an auxiliary stationary process. This leads to studying local times and maximum local times for ergodic sums.",
keywords = "Empirical process, Glivenko–Cantelli theorem, ergodic sums, functional central limit theorem, local times, random walks, sampling",
author = "Guy Cohen and Conze, \{Jean Pierre\}",
note = "Publisher Copyright: {\textcopyright} 2024 Walter de Gruyter GmbH, Berlin/Boston.; Workshops on Ergodic Theory and Dynamical Systems 2021 ; Conference date: 21-06-2021 Through 09-07-2021",
year = "2024",
month = apr,
day = "23",
doi = "10.1515/9783111435503-002",
language = "English",
series = "De Gruyter Proceedings in Mathematics",
publisher = "Walter de Gruyter GmbH",
pages = "13--56",
editor = "Idris Assani",
booktitle = "Ergodic Theory and Dynamical Systems - Proceedings of the Workshops",
address = "Germany",
}