EMPIRICAL PROCESS SAMPLED ALONG A STATIONARY PROCESS
Résumé
Let (X) ∈Z d be a real random field (r.f.) indexed by Z d with common probability distribution function F. Let (z k) ∞ k=0 be a sequence in Z d. The empirical process obtained by sampling the random field along (z k) is n-1 k=0 [1 Xz k ≤s-F (s)]. We give conditions on (z k) implying the Glivenko-Cantelli theorem for the empirical process sampled along (z k) in different cases (independent, associated or weakly correlated random variables). We consider also the functional central limit theorem when the X 's are i.i.d. These conditions are examined when (z k) is provided by an auxiliary stationary process. This leads to investigate local times and maximum local times for ergodic sums.
Mots clés
July 20 2023. 2010 Mathematics Subject Classification. Primary: 60F05 28D05 22D40 60G50
Secondary: 47B15 37A25 37A30 Empirical process sampling along a stationary process local times Glivenko-Cantelli theorem functional central limit theorem random walks
2023. 2010 Mathematics Subject Classification. Primary: 60F05
28D05
22D40
60G50
Secondary: 47B15
37A25
37A30 Empirical process
sampling along a stationary process
local times
Glivenko-Cantelli theorem
functional central limit theorem
random walks
2010 Mathematics Subject Classification. Primary: 60F05 28D05 22D40 60G50
2024. 2010 Mathematics Subject Classification. Primary: 60F05
Domaines
Mathématiques [math]Origine | Fichiers produits par l'(les) auteur(s) |
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