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[{"key": "dc.contributor.author", "value": "Heino, Joonas", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2014-05-08T07:28:32Z", "language": "", "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2014-05-08T07:28:32Z", "language": "", "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2014", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.other", "value": "oai:jykdok.linneanet.fi:1434274", "language": null, "element": "identifier", "qualifier": "other", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/43337", "language": "", "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4m\u00e4n tutkielman tarkoituksena on tutkia Dirichlet'n ongelmaa todenn\u00e4k\u00f6isyysteorian ja peliteorian n\u00e4k\u00f6kulmasta. Osoittautuu, ett\u00e4 k\u00e4yt\u00f6ss\u00e4 olevan alueen reuna vaikuttaa siihen, onko olemassa Dirichlet'n ongelman ratkaisevaa funktiota, joka saavuttaa oikeat reuna-arvot jatkuvasti. Tutkielmassa m\u00e4\u00e4ritell\u00e4\u00e4n joukon reunas\u00e4\u00e4nn\u00f6llisyys jatkuva-aikaisen satunnaisliikkeen avulla. K\u00e4ytt\u00f6kelpoinen ja riitt\u00e4v\u00e4 ehto reunapisteen s\u00e4\u00e4nn\u00f6llisyydelle on Poincar\u00e9n kartioehto. T\u00e4ss\u00e4 ty\u00f6ss\u00e4 n\u00e4ytet\u00e4\u00e4n my\u00f6s Wienerin kriteerio, joka on riitt\u00e4v\u00e4 ja v\u00e4ltt\u00e4m\u00e4t\u00f6n ehto reunapisteen s\u00e4\u00e4nn\u00f6llisyydelle.\r\n\r\nTutkielmassa k\u00e4sitell\u00e4\u00e4n my\u00f6s p-Laplacen yht\u00e4l\u00f6\u00e4 k\u00e4ytt\u00e4en apuna h\u00e4iritty\u00e4 k\u00f6ydenvetopeli\u00e4 (tug-of-war with noise). H\u00e4iritty k\u00f6ydenvetopeli on kahden pelaajan nollasummapeli. Pelaajien arvofunktiot h\u00e4irityss\u00e4 k\u00f6ydenvetopeliss\u00e4 kertovat parhaan mahdollisen odotettavissa olevan tuloksen, pelasi toinen pelaajista kuinka hyvin tahansa. T\u00e4ss\u00e4 ty\u00f6ss\u00e4 n\u00e4ytet\u00e4\u00e4n h\u00e4irityn k\u00f6ydenvetopelin arvofunktioiden yhteys p-harmonisiin funktioihin. Lyhenev\u00e4n askelpituuden h\u00e4iritty k\u00f6ydenvetopeli on k\u00f6ydenvetopelin variaatio, jonka avulla voidaan my\u00f6s tutkia reunas\u00e4\u00e4nn\u00f6llisyytt\u00e4 ja reunafunktioiden resolutiivisuutta.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted using Plone Publishing form by Joonas Heino (jopehein) on 2014-05-08 07:28:31.924866. Form: Pro gradu -lomake (1 tekij\u00e4) (https://kirjasto.jyu.fi/julkaisut/julkaisulomakkeet/pro-gradu-lomake-1-tekijae). JyX data:", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by jyx lomake-julkaisija (jyx-julkaisija@noreply.fi) on 2014-05-08T07:28:32Z\r\nNo. of bitstreams: 2\r\nURN:NBN:fi:jyu-201405081639.pdf: 989212 bytes, checksum: 5632b33af6caa24e90430cc4c0f7aa5e (MD5)\r\nlicense.html: 4895 bytes, checksum: 401bb2cc20ef4c50339aac01e0b4e2a3 (MD5)", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2014-05-08T07:28:32Z (GMT). No. of bitstreams: 2\r\nURN:NBN:fi:jyu-201405081639.pdf: 989212 bytes, checksum: 5632b33af6caa24e90430cc4c0f7aa5e (MD5)\r\nlicense.html: 4895 bytes, checksum: 401bb2cc20ef4c50339aac01e0b4e2a3 (MD5)\r\n Previous issue date: 2014", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "1 verkkoaineisto (84 sivua)", "language": null, "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.format.mimetype", "value": "application/pdf", "language": null, "element": "format", "qualifier": "mimetype", "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": "Brownin liike", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Dirichlet'n ongelma", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "h\u00e4iritty k\u00f6ydenvetopeli", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "p-harmoniset funktiot", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "p-harmonious funktiot", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "stokastinen reunas\u00e4\u00e4nn\u00f6llisyys", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Wienerin kriteerio", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Stokastinen reunas\u00e4\u00e4nn\u00f6llisyys ja h\u00e4iritty k\u00f6ydenvetopeli", "language": null, "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-201405081639", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "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": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "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": "dc.date.updated", "value": "2014-05-08T07:28:33Z", "language": "", "element": "date", 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