{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T15:32:24Z","timestamp":1746804744731,"version":"3.40.5"},"reference-count":30,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11226200","KJ2013Z265"],"award-info":[{"award-number":["11226200","KJ2013Z265"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Research Project of Anhui Province","award":["11226200","KJ2013Z265"],"award-info":[{"award-number":["11226200","KJ2013Z265"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"The equivalent conditions of complete convergence are established for weighted sums of\u03c1<\/mml:mi><\/mml:mrow>~<\/mml:mo><\/mml:mover><\/mml:mrow><\/mml:math>-mixing random variables with different distributions. Our results extend and improve the Baum and Katz complete convergence theorem. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for sequence of\u03c1<\/mml:mi><\/mml:mrow>~<\/mml:mo><\/mml:mover><\/mml:mrow><\/mml:math>-mixing random variables is obtained.<\/jats:p>","DOI":"10.1155\/2014\/612140","type":"journal-article","created":{"date-parts":[[2014,3,19]],"date-time":"2014-03-19T23:02:42Z","timestamp":1395270162000},"page":"1-8","source":"Crossref","is-referenced-by-count":0,"title":["Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of\u03c1<\/mml:mi><\/mml:mrow>~<\/mml:mo><\/mml:mover><\/mml:mrow><\/mml:math>-Mixing Random Variables"],"prefix":"10.1155","volume":"2014","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4420-0023","authenticated-orcid":true,"given":"Chongfeng","family":"Lan","sequence":"first","affiliation":[{"name":"School of Economics and Management, Fuyang Normal College, Fuyang 236037, China"},{"name":"School of Economics and Management, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01046741"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.2307\/2159950"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1023\/A:1021744626773"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022278404634"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2003.12.011"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1155\/2008\/140548"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2007.09.061"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1155\/DDNS\/2006\/27648"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1155\/2007\/74296"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2007.12.020"},{"key":"11","doi-asserted-by":"publisher","DOI":"10. 1155\/2011\/157816"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1155\/2011\/430180"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2012.08.015"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2012.02.069"},{"issue":"3","key":"15","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1007\/s00362-012-0461-2","volume":"54","year":"2013","journal-title":"Statistical Papers"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1155\/2010\/630608"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.33.2.25"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1965-0198524-1"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177704268"},{"issue":"2","key":"20","first-page":"207","volume":"1","year":"1973","journal-title":"Bulletin of the Institute of Mathematics. 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