@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-00716437v2> a dcat:Dataset ;
    dct:description """
              For a stationary random field $(X_j)_{j\\in\\Z^d}$ and some measure m on $\\R^d$, we consider the set-indexed weighted sum process $S_n(A)=\\sum_{j\\in\\Z^d}m(nA\\cap R_j)^\\frac12 X_j$, where R_j is the unit cube with lower corner j. We establish a general invariance principle under a p-stability assumption on the X_j's and an entropy condition on the class of sets A. The limit processes are self-similar set-indexed Gaussian processes with continuous sample paths. Using Chentsov's type representations to choose appropriate measures m and particular sets A, we show that these limits can be Lévy (fractional) Brownian fields or (fractional) Brownian sheets.
            """ ;
    dct:identifier "hal-00716437" ;
    dct:issued "2026-05-12T05:13:18.136443"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-12T05:13:18.136447"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Invariance principles for self-similar set-indexed random fields" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00716437v2/resource/f717e7b7-01f4-4897-9cac-78587063f07d> ;
    dcat:keyword "60f17-60g60-60g18-60g10-60d05",
        "chentsovs-type-representation",
        "dependent-random-field",
        "infoeu-reposemanticsarticle",
        "invariance-principle",
        "journal-articles",
        "levy-fractional-brownian-field",
        "mathmath-prmathematics-mathprobability-mathpr",
        "physical-dependence-measure",
        "set-indexed-process",
        "vapnik-chervonenkis-dimension" ;
    dcat:landingPage <ISSN:%200002-9947> .

<ISSN:%200002-9947> a foaf:Document .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00716437v2/resource/f717e7b7-01f4-4897-9cac-78587063f07d> a dcat:Distribution ;
    dct:format "HTML" ;
    dct:issued "2026-05-12T05:13:18.187494"^^xsd:dateTime ;
    dct:modified "2026-05-12T05:13:18.120930"^^xsd:dateTime ;
    dct:title "Invariance principles for self-similar set-indexed random fields" ;
    dcat:accessURL <https://hal.science/hal-00716437> .

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