@prefix dcat: <http://www.w3.org/ns/dcat#> .
@prefix dct: <http://purl.org/dc/terms/> .
@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix vcard: <http://www.w3.org/2006/vcard/ns#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00834538v1> a dcat:Dataset ;
    dct:description """
              Let $(X_i)_{i\\geq 1}$ be an i.i.d. sequence of mean zero random variables, $S_n:= X_1+\\cdots + X_n$ and $V_n^2:=X_1^2+\\cdots +X_n^2$. We consider four sequences of partial sums processes: the broken lines with vertices at the points $(k/n,S_k/V_n)$ or $(V_k^2/V_n^2,S_k/V_n)$ and the corresponding random step functions. We prove that each of them converges weakly in $C[0,1]$ or $D[0,1]$ to the Brownian motion \\emph{if and only if} $X_1$ belongs to the \\emph{domain of attraction of the normal distribution}. These results contrast with the classical Donsker Prohorov invariance principles where the N.S.C. for such convergences is $\\E X_1^2 < \\infty$.
            """ ;
    dct:identifier "hal-00834538" ;
    dct:issued "2026-05-10T17:09:45.176139"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-10T17:09:45.176143"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Convergence of self-normalized partial sums processes in C[0,1] and D[0,1]" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00834538v1/resource/fa30a5d7-a177-410d-8c94-7ab3bfa6dfb7> ;
    dcat:keyword "ams-60f05-60b05-60g17-60e10",
        "domain-of-attraction",
        "functional-central-limit-theorem",
        "infoeu-reposemanticsarticle",
        "invariance-principle",
        "journal-articles",
        "mathmath-prmathematics-mathprobability-mathpr",
        "self-normalization" ;
    dcat:landingPage <Publications%20Irma%20Lille%20Nouvelle%20Serie> .

<Publications%20Irma%20Lille%20Nouvelle%20Serie> a foaf:Document .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00834538v1/resource/fa30a5d7-a177-410d-8c94-7ab3bfa6dfb7> a dcat:Distribution ;
    dct:format "HTML" ;
    dct:issued "2026-05-10T17:09:45.178839"^^xsd:dateTime ;
    dct:modified "2026-05-10T17:09:45.167150"^^xsd:dateTime ;
    dct:title "Convergence of self-normalized partial sums processes in C[0,1] and D[0,1]" ;
    dcat:accessURL <https://hal.science/hal-00834538> .

<https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> a foaf:Agent ;
    foaf:name "test_moissonnage_selune" .