Conference
EMPIRICAL PROCESS SAMPLED ALONG A STATIONARY PROCESS
| العنوان: | EMPIRICAL PROCESS SAMPLED ALONG A STATIONARY PROCESS |
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| المؤلفون: | Cohen, Guy, Conze, Jean-Pierre |
| المساهمون: | Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut Agro Rennes Angers, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro) |
| المصدر: | Workshop Ergodic Theory (Chapel-Hill) ; https://hal.science/hal-04380332 ; Workshop Ergodic Theory (Chapel-Hill), De Gruyter, pp.13-56, 2024, ⟨10.1515/9783111435503-002⟩ |
| بيانات النشر: | HAL CCSD De Gruyter |
| سنة النشر: | 2024 |
| المجموعة: | Archive Ouverte de l'Université Rennes (HAL) |
| مصطلحات موضوعية: | 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, [MATH]Mathematics [math] |
| الوصف: | International audience ; 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. |
| نوع الوثيقة: | conference object |
| اللغة: | English |
| DOI: | 10.1515/9783111435503-002 |
| الاتاحة: | https://hal.science/hal-04380332 https://hal.science/hal-04380332v1/document https://hal.science/hal-04380332v1/file/empiric%20sampled.pdf https://doi.org/10.1515/9783111435503-002 |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.42218308 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1515/9783111435503-002 |
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