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Proceedings/Recueil Des Communications Année : 2024

EMPIRICAL PROCESS SAMPLED ALONG A STATIONARY PROCESS

Guy Cohen
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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.
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Dates et versions

hal-04380332 , version 1 (08-01-2024)

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  • HAL Id : hal-04380332 , version 1

Citer

Guy Cohen, Jean-Pierre Conze. EMPIRICAL PROCESS SAMPLED ALONG A STATIONARY PROCESS. Workshop Ergodic Theory (Chapel-Hill), 2024. ⟨hal-04380332⟩
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