@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-00595912v5> a dcat:Dataset ;
    dct:description """
              Let $(X,\\p_x)$ be a continuous time Markov chain with finite or countable state space $S$ and let $T$ be its first passage time in a subset $D$ of $S$. It is well known that if $\\mu$ is a quasi-stationary distribution relatively to $T$, then this time is exponentially distributed under $\\p_\\mu$. However, quasi-stationarity is not a necessary condition. In this paper, we determine more general conditions on an initial distribution $\\mu$ for $T$ to be exponentially distributed under $\\p_\\mu$. We show in addition how quasi-stationary distributions can be expressed in terms of any initial law which makes the distribution of $T$ exponential. We also study two examples in branching processes where exponentiality does imply quasi-stationarity.
            """ ;
    dct:identifier "hal-00595912" ;
    dct:issued "2026-05-09T06:41:20.233489"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-09T06:41:20.233493"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Exponentiality of first passage times of continuous time Markov chains" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00595912v5/resource/6da6f764-5e8a-4c5b-977c-56907d0def3b> ;
    dcat:keyword "92d25-60j28",
        "exponential-decay",
        "first-passage-time",
        "infoeu-reposemanticspreprint",
        "mathmath-prmathematics-mathprobability-mathpr",
        "preprints-working-papers-",
        "quasi-stationary-distribution" ;
    dcat:landingPage <https://hal.science/hal-00595912> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00595912v5/resource/6da6f764-5e8a-4c5b-977c-56907d0def3b> a dcat:Distribution ;
    dct:format "HTML" ;
    dct:issued "2026-05-09T06:41:20.245402"^^xsd:dateTime ;
    dct:modified "2026-05-09T06:41:20.223158"^^xsd:dateTime ;
    dct:title "Exponentiality of first passage times of continuous time Markov chains" ;
    dcat:accessURL <https://hal.science/hal-00595912> .

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

<https://hal.science/hal-00595912> a foaf:Document .