{"created":"2022-01-28T01:12:19.760969+00:00","id":2005448,"links":{},"metadata":{"_buckets":{"deposit":"27f4f09a-bd6f-4b5c-83b4-fa09ad690fd1"},"_deposit":{"id":"2005448","owners":[1],"pid":{"revision_id":0,"type":"depid","value":"2005448"},"status":"published"},"_oai":{"id":"oai:u-ryukyu.repo.nii.ac.jp:02005448","sets":["1642838403123","1642838403551:1642838406414"]},"author_link":[],"item_1617186331708":{"attribute_name":"Title","attribute_value_mlt":[{"subitem_1551255647225":"ジャンプ型マルコフ過程の再帰性、推移確率のモーメント等に関する研究","subitem_1551255648112":"ja"},{"subitem_1551255647225":"Studies on recurrence and moments of transition probabilities of jump type Markov processes","subitem_1551255648112":"en"}]},"item_1617186419668":{"attribute_name":"Creator","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"山里, 眞","creatorNameLang":"ja"}]},{"creatorNames":[{"creatorName":"陳, 春航","creatorNameLang":"ja"}]},{"creatorNames":[{"creatorName":"杉浦, 誠","creatorNameLang":"ja"}]},{"creatorNames":[{"creatorName":"Yamazato, Makoto","creatorNameLang":"en"}]},{"creatorNames":[{"creatorName":"Chen, Chunhang","creatorNameLang":"en"}]},{"creatorNames":[{"creatorName":"Sugiura, Makoto","creatorNameLang":"en"}]}]},"item_1617186476635":{"attribute_name":"Access Rights","attribute_value_mlt":[{"subitem_1522299639480":"open access","subitem_1600958577026":"http://purl.org/coar/access_right/c_abf2"}]},"item_1617186609386":{"attribute_name":"Subject","attribute_value_mlt":[{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"storage process"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"tail behavior"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"local time"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"hitting time"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"recurrence"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"moment"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"skip free process"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"OU type process"},{"subitem_1522299896455":"ja","subitem_1522300014469":"Other","subitem_1523261968819":"モーメント"},{"subitem_1522299896455":"ja","subitem_1522300014469":"Other","subitem_1523261968819":"加法過程"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"Levy measure"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"subexponentiality"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"submultiplicativity"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"skip-free process"},{"subitem_1522299896455":"ja","subitem_1522300014469":"Other","subitem_1523261968819":"再帰性"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"subadditive functional"}]},"item_1617186626617":{"attribute_name":"Description","attribute_value_mlt":[{"subitem_description":"科研費番号: 13640127","subitem_description_type":"Other"},{"subitem_description":"平成13年度～平成15年度科学研究費補助金(基盤研究(C)(2))研究成果報告書","subitem_description_type":"Other"},{"subitem_description":"研究概要：本研究による主な研究成果は以下のとおりである. 1.Skip free Levy processのhitting time processのレヴィ測度を拡張された意味でのlocal timeによって表現した.この結果は,local timeの拡張としてどのようなものが自然なのかという問題に対するひとつの解答になっている.結果は簡単な形であり証明も短いがこれまでこのような結果は知られていないようである.また,hitting timeのレヴィ測度をprocessの推移確率が連続特異である場合を除いて推移確率の確率関数やHawksの導入した標準密度関数で表した. 2.リャプーノフ関数をうまくとることによりstorage processの再帰性および非再帰性に関する新しい十分条件を入力(input process)のレヴィ測度と出力(release rate)によってそれぞれ与えた.これによりinput processがstable processでrelease rateが巾関数の場合には再帰的なための必要十分条件が得られた.またrelease rateが有界な場合の再帰的および非再帰的のためのこれまで知られている十分条件を精密にした.その一部の結果はベッセル過程の再帰および非再帰に対応することも指摘した. 3.Storage processの推移確率の一般化モーメントが存在する(存在しない)ための条件をinput processのレヴィ測度の一般化モーメントの存在(非存在)条件で与えた. 4.Storage processの推移確率の末尾部の漸近挙動とinput processのレヴィ測度の末尾部の漸近挙動との関係を与えた.この結果を得るには無限分解可能分布のChistyakovらが考えた subexponentialityおよびRosinskiやSamorodnitkyらが考えた確率過程のsubadditivityという概念とそれらの性質が有用であった. 3のモーメントと4の末尾部の漸近挙動の結果に共通していて興味深いことはOrnstein-Uhlenbeck type process (release rateが一次関数の場合)を境界として推移確率とレヴィ測度との対応関係が大きく異なることである.即ちrelease rateが巾関数でその巾の次数が1以下の場合には条件は加法過程の場合と同じで次数は関係しないが次数が1より大きい場合には次数も条件に関係してくる。","subitem_description_type":"Other"},{"subitem_description":"研究概要：Main results of this research are the following : 1. We gave representations of the Levy measureof the hitting time process of skip free Levy process in terms of its local time. This result is an answer to a question what is a natural generalization of the continuous local time to discontinuous one. While the result is simple and the proof is short, the result seems new. Moreover, we represented the Levy measure of the hitting time process by the probability function or the canonical density of the transition probability in case that the transition probability is discrete or absolutely continuous, respectively. 2. We gave new sufficient conditions for recurrence and transience of storage process in terms of Levy measure of its input process and release rate. By applying this result we obtained the necessary and sufficient condition for recurrence in case thatthe input process is stable process and the release rate is a power function. We improved known sufficient conditions for recurrence and transience in case that the release rate is bounded.We pointed out that a part of the result corresponds to the recurrence-transience condition for Bessel processes. 3. We gave conditions for the existence(nonexistence)of general ized moments of storage prooess in terms of the existence(nonexistence)of the generalized moments of the Levy measure of its input process. 4. We gave relations between the tail behavior of the transition probability of storage process and the tail behavior of the Levy measure of its input process. In order to obtain this result, the concept subexponentiality, which was given by Chistyakov, and subadditivity, which is considered by Rosinsky and Samorodnitky, were useful. Interesting phenomenon common in 2, 3 and 4 is that Ornstein-UhLenbeck type process plays a critical role in case the release rate is a power function.","subitem_description_type":"Other"},{"subitem_description":"未公開：P.1以降(別刷論文のため)","subitem_description_type":"Other"},{"subitem_description":"研究報告書","subitem_description_type":"Other"}]},"item_1617186643794":{"attribute_name":"Publisher","attribute_value_mlt":[{"subitem_1522300295150":"ja","subitem_1522300316516":"山里眞"}]},"item_1617186702042":{"attribute_name":"Language","attribute_value_mlt":[{"subitem_1551255818386":"jpn"}]},"item_1617186783814":{"attribute_name":"Identifier","attribute_value_mlt":[{"subitem_identifier_type":"HDL","subitem_identifier_uri":"http://hdl.handle.net/20.500.12000/16167"}]},"item_1617186920753":{"attribute_name":"Source Identifier","attribute_value_mlt":[{"subitem_1522646500366":"NCID","subitem_1522646572813":"BA74311088"}]},"item_1617187056579":{"attribute_name":"Bibliographic Information","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2004-04","bibliographicIssueDateType":"Issued"}}]},"item_1617258105262":{"attribute_name":"Resource Type","attribute_value_mlt":[{"resourcetype":"research report","resourceuri":"http://purl.org/coar/resource_type/c_18ws"}]},"item_1617265215918":{"attribute_name":"Version Type","attribute_value_mlt":[{"subitem_1522305645492":"VoR","subitem_1600292170262":"http://purl.org/coar/version/c_970fb48d4fbd8a85"}]},"item_1617605131499":{"attribute_name":"File","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_access","filename":"13640127.pdf","mimetype":"application/pdf","url":{"objectType":"fulltext","url":"https://u-ryukyu.repo.nii.ac.jp/record/2005448/files/13640127.pdf"},"version_id":"150180ac-33e2-4f10-8cf4-e182bb2ea2e4"}]},"item_title":"ジャンプ型マルコフ過程の再帰性、推移確率のモーメント等に関する研究","item_type_id":"15","owner":"1","path":["1642838403123","1642838406414"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2010-03-08"},"publish_date":"2010-03-08","publish_status":"0","recid":"2005448","relation_version_is_last":true,"title":["ジャンプ型マルコフ過程の再帰性、推移確率のモーメント等に関する研究"],"weko_creator_id":"1","weko_shared_id":-1},"updated":"2022-10-31T02:42:40.883837+00:00"}