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1",{},{"id":506,"createTime":507,"updateTime":507,"relativeEntities":508,"slug":509,"properties":510,"entityType":121,"verifyStatus":122,"verifyTime":507,"verifyNote":123,"languages":521,"translateLanguages":24,"viewCount":25,"primaryUrl":522,"fullTextUrl":24,"authors":523,"publicationType":145,"publisherRelationship":581,"citationCount":635,"citationInfo":636,"publishDate":642,"publishYear":637,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":643,"openAccess":24,"references":644,"isForceReanalyzing":247},"c67607a3-a029-4d64-aa7b-95788d889820","2024-12-10T09:08:52.680+00:00",[],"Advances-in-Complete-Mixability",{"openalex":511,"mag":513,"abstract":515,"title":517,"doi":519},{"VOID":512},"W2000473663",{"VOID":514},"2000473663",{"EN":516},"\u003Cjats:p>The concept of complete mixability is relevant to some problems of optimal couplings with important applications in quantitative risk management. In this paper we prove new properties of the set of completely mixable distributions, including a completeness and a decomposition theorem. 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process whose parameter \u003Cjats:italic>t\u003C\u002Fjats:italic> runs over a finite or infinite n terval \u003Cjats:italic>T.\u003C\u002Fjats:italic> Let \u003Cjats:italic>t\u003C\u002Fjats:italic>\u003Cjats:sub>1\u003C\u002Fjats:sub>\u003Cjats:italic>, t\u003C\u002Fjats:italic>\u003Cjats:sub>2\u003C\u002Fjats:sub> ɛ T, \u003Cjats:italic>t\u003C\u002Fjats:italic>\u003Cjats:sub>1\u003C\u002Fjats:sub> 〈 t\u003Cjats:sub>2\u003C\u002Fjats:sub>; the random variable \u003Cjats:italic>X\u003C\u002Fjats:italic>(\u003Cjats:italic>t\u003C\u002Fjats:italic>\u003Cjats:sub>2\u003C\u002Fjats:sub>) \u003Cjats:italic>– X\u003C\u002Fjats:italic>(\u003Cjats:italic>t\u003C\u002Fjats:italic>\u003Cjats:sub>1\u003C\u002Fjats:sub>) is called the increment of the process \u003Cjats:italic>X\u003C\u002Fjats:italic>(\u003Cjats:italic>t\u003C\u002Fjats:italic>) over the interval [\u003Cjats:italic>t\u003C\u002Fjats:italic>\u003Cjats:sub>1\u003C\u002Fjats:sub>, 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A process \u003Cjats:italic>X\u003C\u002Fjats:italic>(\u003Cjats:italic>t\u003C\u002Fjats:italic>) is said to be homogeneous if the distribution function of the increment \u003Cjats:italic>X\u003C\u002Fjats:italic>(\u003Cjats:italic>t\u003C\u002Fjats:italic> + τ) — \u003Cjats:italic>X\u003C\u002Fjats:italic>(\u003Cjats:italic>t\u003C\u002Fjats:italic>) depends only on the length τ of the interval but is independent of the endpoint \u003Cjats:italic>t.\u003C\u002Fjats:italic> Two intervals are said to be non-overlapping if they have no interior point in common. A process \u003Cjats:italic>X\u003C\u002Fjats:italic>(\u003Cjats:italic>t\u003C\u002Fjats:italic>) is called a process with independent increments if the increments over non-overlapping intervals are stochastically independent. A process \u003Cjats:italic>X\u003C\u002Fjats:italic>(\u003Cjats:italic>t\u003C\u002Fjats:italic>) is said to be continuous at the point \u003Cjats:italic>t\u003C\u002Fjats:italic> if plim\u003Cjats:sub>τ→0\u003C\u002Fjats:sub> [\u003Cjats:italic>X\u003C\u002Fjats:italic>(\u003Cjats:italic>t\u003C\u002Fjats:italic> + τ) — \u003Cjats:italic>X\u003C\u002Fjats:italic>(\u003Cjats:italic>t\u003C\u002Fjats:italic>)] = 0, that is if for any ε > 0, lim\u003Cjats:sub>τ→0\u003C\u002Fjats:sub>\u003Cjats:italic>P\u003C\u002Fjats:italic>(| \u003Cjats:italic>X\u003C\u002Fjats:italic>(\u003Cjats:italic>t\u003C\u002Fjats:italic> + τ) — \u003Cjats:italic>X\u003C\u002Fjats:italic>(\u003Cjats:italic>t\u003C\u002Fjats:italic>) | > ε) = 0. A process is continuous in an interval [\u003Cjats:italic>A, B\u003C\u002Fjats:italic>] if it is continuous in every point of [\u003Cjats:italic>A, B\u003C\u002Fjats:italic>].\u003C\u002Fjats:p>",{"EN":676},"A characterization of stable processes",{"VOID":678},"10.2307\u002F3212010","2024-12-04T03:42:40.826+00:00",[125],"https:\u002F\u002Fwww.cambridge.org\u002Fcore\u002Fproduct\u002Fidentifier\u002FS0021900200032915\u002Ftype\u002Fjournal_article",[683],{"id":684,"sortIndex":25,"researcher":24,"roles":685,"affiliations":686,"properties":695,"displayName":697,"givenName":24,"familyName":24},"627c36ad-a6f1-470f-8e33-400d6cdf6b9d",[],[687],{"id":688,"sortIndex":25,"affiliation":689,"properties":24},"3c7ddb69-3717-4601-8e0b-f8c2d8d03ea4",{"id":688,"createTime":24,"updateTime":24,"relativeEntities":690,"slug":24,"properties":691,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":694,"statistic":24},[],{"title":692},{"VI":693},"Catholic University of America",[],{"title":696,"openalex":698},{"EN":697},"Eugene Lukács",{"VOID":699},"A5111775413",{"url":24,"publisher":701,"properties":747},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":702,"slug":10,"properties":703,"entityType":22,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":25,"subjectFields":708,"manageAffiliations":721,"indexDatabases":732,"url":97,"thumbnailPath":24,"statistic":24,"gsStatistic":24,"type":24,"analyzePriority":24},[],{"country":704,"eissn":705,"issn":706,"title":707},{"VOID":13},{"VOID":15},{"VOID":17},{"EN":19},[709,713,717],{"id":28,"createTime":24,"updateTime":24,"relativeEntities":710,"label":711,"description":712,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":31},{},{"id":34,"createTime":24,"updateTime":24,"relativeEntities":714,"label":715,"description":716,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":37},{},{"id":40,"createTime":24,"updateTime":24,"relativeEntities":718,"label":719,"description":720,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":43},{},[722,727],{"id":47,"createTime":24,"updateTime":24,"relativeEntities":723,"slug":24,"properties":724,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":726,"statistic":24},[],{"title":725},{"EN":51},[],{"id":54,"createTime":24,"updateTime":24,"relativeEntities":728,"slug":24,"properties":729,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":731,"statistic":24},[],{"title":730},{"EN":58},[],[733,740],{"id":62,"indexDatabase":734,"url":73,"indexYears":74,"academicFieldIds":739,"indexDatabaseRanking":79},{"id":64,"createTime":24,"updateTime":24,"relativeEntities":735,"label":736,"description":737,"key":70,"publicationTags":738,"standard":24},[],{"EN":67,"VI":67},{"EN":67,"VI":69},[72],[76,77,78],{"id":81,"indexDatabase":741,"url":94,"indexYears":24,"academicFieldIds":746,"indexDatabaseRanking":24},{"id":83,"createTime":24,"updateTime":24,"relativeEntities":742,"label":743,"description":744,"key":90,"publicationTags":745,"standard":24},[],{"EN":86,"VI":86},{"EN":88,"VI":89},[92,93],[96],{"issue":748,"pages":749,"volume":751},{"VOID":630},{"VOID":750},"409-418",{"VOID":752},"6",48,{"total":753,"publishYear":755,"statisticByYear":756},1969,{"2013":204,"2014":204,"2016":205,"2017":757,"2021":204,"2022":204,"2023":204},19,"1969-08-01",[92],[761,764,767,770],{"id":24,"text":762,"url":24,"identifiers":763},"Lukacs, 1967, Une caractérisation des processus stables et symmétriques, C.R. Acad. Sci. Paris, 264, 959",{},{"id":24,"text":765,"url":24,"identifiers":766},"LoèVe, 1963, Probability Theory.",{},{"id":24,"text":768,"url":24,"identifiers":769},"10.1214\u002Faoms\u002F1177730437",{"doi":768},{"id":24,"text":771,"url":24,"identifiers":772},"Lukacs E. (1968) Stochastic Convergence. Heath Mathematical Monographs. 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The models for oil exploration strategies that were discussed by Benkherouf and Bather (1988) are reinterpreted as current-age models for discrete renewal processes. 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Alternative models for the distribution are given.\u003C\u002Fjats:p>",{"EN":1187},"Absorption sampling and the absorption distribution",{"VOID":1189},"10.1017\u002Fs0021900200015114",[125],"https:\u002F\u002Fwww.cambridge.org\u002Fcore\u002Fproduct\u002Fidentifier\u002FS0021900200015114\u002Ftype\u002Fjournal_article",[1193],{"id":1194,"sortIndex":25,"researcher":24,"roles":1195,"affiliations":1196,"properties":1203,"displayName":806,"givenName":24,"familyName":24},"8aed820a-a596-4f62-a6ad-e01c6f8c85b7",[],[1197],{"id":797,"sortIndex":25,"affiliation":1198,"properties":24},{"id":797,"createTime":24,"updateTime":24,"relativeEntities":1199,"slug":24,"properties":1200,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1202,"statistic":24},[],{"title":1201},{"EN":802},[],{"title":1204,"openalex":1205},{"EN":806},{"VOID":808},{"url":24,"publisher":1207,"properties":1253},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":1208,"slug":10,"properties":1209,"entityType":22,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":25,"subjectFields":1214,"manageAffiliations":1227,"indexDatabases":1238,"url":97,"thumbnailPath":24,"statistic":24,"gsStatistic":24,"type":24,"analyzePriority":24},[],{"country":1210,"eissn":1211,"issn":1212,"title":1213},{"VOID":13},{"VOID":15},{"VOID":17},{"EN":19},[1215,1219,1223],{"id":28,"createTime":24,"updateTime":24,"relativeEntities":1216,"label":1217,"description":1218,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":31},{},{"id":34,"createTime":24,"updateTime":24,"relativeEntities":1220,"label":1221,"description":1222,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":37},{},{"id":40,"createTime":24,"updateTime":24,"relativeEntities":1224,"label":1225,"description":1226,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":43},{},[1228,1233],{"id":47,"createTime":24,"updateTime":24,"relativeEntities":1229,"slug":24,"properties":1230,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1232,"statistic":24},[],{"title":1231},{"EN":51},[],{"id":54,"createTime":24,"updateTime":24,"relativeEntities":1234,"slug":24,"properties":1235,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1237,"statistic":24},[],{"title":1236},{"EN":58},[],[1239,1246],{"id":62,"indexDatabase":1240,"url":73,"indexYears":74,"academicFieldIds":1245,"indexDatabaseRanking":79},{"id":64,"createTime":24,"updateTime":24,"relativeEntities":1241,"label":1242,"description":1243,"key":70,"publicationTags":1244,"standard":24},[],{"EN":67,"VI":67},{"EN":67,"VI":69},[72],[76,77,78],{"id":81,"indexDatabase":1247,"url":94,"indexYears":24,"academicFieldIds":1252,"indexDatabaseRanking":24},{"id":83,"createTime":24,"updateTime":24,"relativeEntities":1248,"label":1249,"description":1250,"key":90,"publicationTags":1251,"standard":24},[],{"EN":86,"VI":86},{"EN":88,"VI":89},[92,93],[96],{"issue":1254,"pages":1256,"volume":1258},{"VOID":1255},"02",{"VOID":1257},"489-494",{"VOID":1259},"35",{"total":639,"publishYear":1261,"statisticByYear":1262},1998,{"2014":204},"1998-06-01",[79,92],[1266,1269,1272,1275,1278,1281,1284,1287,1289,1292,1295,1298,1301],{"id":24,"text":1267,"url":24,"identifiers":1268},"1981, Commun. 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The goal of this paper is to establish the strong law of large numbers for a sequence of END and identically distributed random variables. In doing so we derive some new inequalities of large deviation type for the sums of END and identically distributed random variables being suitably truncated. We also show applications of our main result to risk theory and renewal theory.\u003C\u002Fjats:p>",{"EN":1317},"The Strong Law of Large Numbers for Extended Negatively Dependent Random Variables",{"VOID":1319},"10.1239\u002Fjap\u002F1294170508",[125],"https:\u002F\u002Fwww.cambridge.org\u002Fcore\u002Fproduct\u002Fidentifier\u002FS0021900200007257\u002Ftype\u002Fjournal_article",[1323,1342,1361],{"id":1324,"sortIndex":25,"researcher":24,"roles":1325,"affiliations":1326,"properties":1335,"displayName":1339,"givenName":24,"familyName":24},"923ea80c-3702-49c2-a300-422b6d99e455",[],[1327],{"id":1328,"sortIndex":25,"affiliation":1329,"properties":24},"b2b7be9c-9507-4691-82f6-0bb0150b961a",{"id":1328,"createTime":24,"updateTime":24,"relativeEntities":1330,"slug":24,"properties":1331,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1334,"statistic":24},[],{"title":1332},{"VI":1333},"University of 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