{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T15:48:58Z","timestamp":1774626538043,"version":"3.50.1"},"reference-count":6,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2016,7,14]],"date-time":"2016-07-14T00:00:00Z","timestamp":1468454400000},"content-version":"unspecified","delay-in-days":9905,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Probability"],"published-print":{"date-parts":[[1989,6]]},"abstract":"<jats:p>In this paper we consider an independent and identically distributed sequence {<jats:italic>Y<jats:sub>n<\/jats:sub><\/jats:italic>} with common distribution function <jats:italic>F<\/jats:italic>(<jats:italic>x<\/jats:italic>) and a random variable <jats:italic>X<\/jats:italic><jats:sub>0<\/jats:sub>, independent of the <jats:italic>Y<jats:sub>i<\/jats:sub><\/jats:italic>'s, and define a Markovian sequence {<jats:italic>X<jats:sub>n<\/jats:sub><\/jats:italic>} as <jats:italic>X<jats:sub>i<\/jats:sub><\/jats:italic> = <jats:italic>X<\/jats:italic><jats:sub>0<\/jats:sub>, if <jats:italic>i<\/jats:italic> = 0, <jats:italic>X<jats:sub>i<\/jats:sub><\/jats:italic> = <jats:italic>k<\/jats:italic> max{<jats:italic>X<jats:sub>i<\/jats:sub><\/jats:italic><jats:sub>\u2212 1<\/jats:sub>, <jats:italic>Y<jats:sub>i<\/jats:sub><\/jats:italic>}, if <jats:italic>i<\/jats:italic> \u2267 1, <jats:italic>k<\/jats:italic> \u2208 R, 0 &lt; <jats:italic>k<\/jats:italic> &lt; 1. For this sequence we evaluate basic distributional formulas and give conditions on <jats:italic>F<\/jats:italic>(<jats:italic>x<\/jats:italic>) for the sequence to possess a stationary distribution. We prove that for any distribution function <jats:italic>H<\/jats:italic>(<jats:italic>x<\/jats:italic>) with left endpoint greater than or equal to zero for which log <jats:italic>H<\/jats:italic>(<jats:italic>e<jats:sup>x<\/jats:sup><\/jats:italic>) is concave it is possible to construct such a stationary sequence with marginal distributions equal to it. We study the limit laws for extremes and <jats:italic>k<\/jats:italic>th order statistics.<\/jats:p>","DOI":"10.2307\/3214030","type":"journal-article","created":{"date-parts":[[2006,4,24]],"date-time":"2006-04-24T14:40:28Z","timestamp":1145889628000},"page":"219-232","source":"Crossref","is-referenced-by-count":49,"title":["An extremal markovian sequence"],"prefix":"10.1017","volume":"26","author":[{"given":"M. Teresa","family":"Alpuim","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,7,14]]},"reference":[{"key":"S0021900200027236_ref6","doi-asserted-by":"publisher","DOI":"10.1017\/S0021900200097436"},{"key":"S0021900200027236_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00532484"},{"key":"S0021900200027236_ref1","volume-title":"The Asymptotic Theory of Extreme Order Statistics.","author":"Galambos","year":"1978"},{"key":"S0021900200027236_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/BF02888564"},{"key":"S0021900200027236_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5449-2"},{"key":"S0021900200027236_ref4","first-page":"1","article-title":"An extreme-Markovian-stationary sequence, quick statistical decision","volume":"XXV","author":"Tiago De Oliveira","year":"1972","journal-title":"Metron"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900200027236","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,19]],"date-time":"2019-05-19T16:16:41Z","timestamp":1558282601000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900200027236\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,6]]},"references-count":6,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1989,6]]}},"alternative-id":["S0021900200027236"],"URL":"https:\/\/doi.org\/10.2307\/3214030","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,6]]}}}