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[{"key": "dc.contributor.advisor", "value": "Parviainen, Mikko", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "K\u00f6ykk\u00e4, Jenni", "language": "", "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2024-08-01T05:12:08Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2024-08-01T05:12:08Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2024", "language": "", "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/96456", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4ss\u00e4 tutkielmassa tutustutaan optimaalisen kontrollin ongelmiin sek\u00e4\nsatunnaispeleihin osittaisdifferentiaaliyht\u00e4l\u00f6iden (ODY:jen) avulla. Tutkielma jakautuu kolmeen osaan, joista ensimm\u00e4isess\u00e4 k\u00e4sitell\u00e4\u00e4n kontrolliteoriaa, sek\u00e4 etenkin Bellmanin dynaamisen ohjelmoinnin periaatetta (DOP).\nDOP:n avulla usein monimutkaiset optimointiongelmat voidaan jakaa pienempiin osaongelmiin. Lis\u00e4ksi DOP:n avulla saadaan n\u00e4ytetty\u00e4 arvofunktion olevan yksik\u00e4sitteinen viskositeettiratkaisu ODY:lle nimelt\u00e4 HamiltonJacobi-Bellman-yht\u00e4l\u00f6, joten ODY-teoriaa voidaan soveltaa tietynlaisten kontrolliongelmien ratkaisemiseksi.\nToisessa osassa tutustutaan stokastiikan ja ODY:jen yhteyteen satunnaisk\u00e4velyn ja Laplacen yht\u00e4l\u00f6n kautta. Ensin todistetaan, ett\u00e4 funktio on\nharmoninen, eli ratkaisu Laplacen yht\u00e4l\u00f6lle, jos ja vain jos se toteuttaa keskiarvoperiaatteen. T\u00e4m\u00e4n j\u00e4lkeen n\u00e4ytet\u00e4\u00e4n, ett\u00e4 satunnaisk\u00e4velyn arvo tietyss\u00e4 pisteess\u00e4 toteuttaa keskiarvoperiaatteen, jolloin saadaan luotua yhteys\nODY:jen ja satunnaisk\u00e4velyn v\u00e4lille. T\u00e4ss\u00e4 tilanteessa keskiarvoperiaate voidaan tulkita ehdollisen odotusarvon kautta.\nKolmannessa osassa tarkastellaan satunnaiskohinallista k\u00f6ydenvetopeli\u00e4\nja p-Laplacen yht\u00e4l\u00f6\u00e4. K\u00f6ydenvetopelille saadaan rakennettua (p, \u03b5)-harmoninen\narvofunktiokandidaatti dynaamisen ohjelmoinnin periaatteen avulla. Kappaleessa saadaan todistettua (p, \u03b5)-harmonisten funktioiden tasaisesti suppenevan jonon rajafunktion olevan yksik\u00e4sitteinen viskositeettiratkaisu pLaplacen yht\u00e4l\u00f6lle. Lis\u00e4ksi Arzel\u00e1-Ascolin muunnelmalla p\u00e4\u00e4st\u00e4\u00e4n todistamaan pelin arvofunktioiden muodostaman jonon suppenevan tasaisesti, kun\notetaan raja-arvo \u03b5 \u2192 0.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2024-08-01T05:12:07Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2024-08-01T05:12:08Z (GMT). No. of bitstreams: 0\n Previous issue date: 2024", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "75", "language": "", "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.language.iso", "value": "fin", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "optimaalinen kontrolli", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "stokastiset pelit", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "k\u00f6ydenvetopelit", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "p-Laplacen yht\u00e4l\u00f6", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "viskositeettiratkaisut", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Stokastiset pelit, optimaalinen kontrolli ja osittaisdifferentiaaliyht\u00e4l\u00f6t", "language": "", "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-202408015278", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Matematiikan ja tilastotieteen laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Mathematics and Statistics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Matematiikka", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Mathematics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "yvv.contractresearch.funding", "value": "0", "language": "", "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": null, "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4041", "language": "", "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matematiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "osittaisdifferentiaaliyht\u00e4l\u00f6t", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}]
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