{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1390282680248052480.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.2996/kmj/1071674463"}},{"identifier":{"@type":"MRID","@value":"1942780"}},{"identifier":{"@type":"NAID","@value":"130003426774"}}],"dc:title":[{"@language":"en","@value":"A local limit theorem for random walk defined on a finite Markov chain with absorbing barriers"}],"dc:language":"en","description":[{"type":"abstract","notation":[{"@language":"en","@value":"Let {ξ<SUB><I>n</I></SUB>}<SUB><I>n</I>≥0</SUB> denote an ergodic Markov chain with a finite state space <B>Ξ</B>={1, 2, ..., <I>s</I>}. For each <I>j</I>, <I>k</I>∈<B>Ξ</B>, let {<I>Y</I><SUB><I>n</I></SUB><SUP><I>jk</I></SUP>}<SUB><I>n</I>≥1</SUB> be a sequence of i.i.d. {−1, 1}-valued random variables which are independent of {ξ<SUB><I>n</I></SUB>}. We define the process {<I>S</I><SUB><I>n</I></SUB>}<SUB><I>n</I>≥ 0</SUB> by <I>S</I><SUB>0</SUB>=0 and <I>S</I><SUB><I>n</I></SUB>=<I>S</I><SUB><I>n</I>−1</SUB>+<I>Y</I><SUB><I>n</I></SUB><SUP>ξ<SUB><I>n</I>−1</SUB>ξ<SUB><I>n</I></SUB></SUP> for <I>n</I>≥ 1. Let <I>a</I> be a positive integer. We denote by <I>T</I><SUB><I>x</I></SUB> the first exit time of the process from the interval [−<I>x</I>, <I>a</I>−<I>x</I>] for each <I>x</I>=0, 1, ..., <I>a</I>. We give an asymptotic behaviour of the transition functions <B><I>P</I></B><SUB><I>jk</I></SUB><SUP>(<I>n</I>)</SUP>(<I>x</I>, <I>y</I>)=<B><I>P</I></B>{<I>x</I>+<I>S</I><SUB><I>n</I></SUB>=<I>y</I>; <I>T</I><SUB><I>x</I></SUB>><I>n</I>; ξ<SUB><I>n</I></SUB>=<I>k|</I>ξ<SUB>0</SUB>=<I>j</I>} as <I>n</I>→∞ for each <I>x</I>, <I>y</I>∈[0, <I>a</I>] and all <I>j</I>, <I>k</I>∈<B>Ξ</B>."}],"abstractLicenseFlag":"disallow"}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1410282680248052481","@type":"Researcher","personIdentifier":[{"@type":"NRID","@value":"9000252837668"}],"foaf:name":[{"@language":"en","@value":"Shimura Michio"}]},{"@id":"https://cir.nii.ac.jp/crid/1410282680248052480","@type":"Researcher","personIdentifier":[{"@type":"NRID","@value":"9000252837667"}],"foaf:name":[{"@language":"en","@value":"Takenami Toshiyuki"}]}],"publication":{"publicationIdentifier":[{"@type":"PISSN","@value":"03865991"},{"@type":"LISSN","@value":"03865991"},{"@type":"EISSN","@value":"18815472"}],"prism:publicationName":[{"@language":"en","@value":"Kodai Mathematical Journal"},{"@language":"ja","@value":"ＫＯＤＡＩ　ＭＡＴＨＥＭＡＴＩＣＡＬ　ＪＯＵＲＮＡＬ"},{"@language":"en","@value":"KODAI MATH. J."},{"@language":"en","@value":"KMJ"},{"@language":"ja","@value":"ＫＭＪ"},{"@language":"en","@value":"KODAI MATHEMATICAL JOURNAL"}],"dc:publisher":[{"@language":"en","@value":"Institute of Science Tokyo, Department of Mathematics"},{"@language":"ja","@value":"国立大学法人 東京科学大学理学院数学系"}],"prism:publicationDate":"2002","prism:volume":"25","prism:number":"3","prism:startingPage":"301","prism:endingPage":"308"},"reviewed":"false","availableAt":"2002","foaf:topic":[{"@id":"https://cir.nii.ac.jp/all?q=General%20Mathematics","dc:title":"General Mathematics"}],"dataSourceIdentifier":[{"@type":"JALC","@value":"oai:japanlinkcenter.org:1001319583"},{"@type":"CROSSREF","@value":"10.2996/kmj/1071674463"},{"@type":"CIA","@value":"130003426774"}]}