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The\ntails of X are not regularly varying and the sequence Sn of \naccumulated gains has,\nsuitably centered and normalized, a class of semistable laws as \nsubsequential limit\ndistributions (Martin-L¨of (1985), Cs¨org˝o and Dodunekova (1991)). \nThis has led to\na clarification of the paradox and an interesting and unusual \nasymptotic theory in\npast decades. In this paper we prove that Sn can be approximated by \na semistable\nL´evy process {L(n), n ≥ 1} with a.s. error O(\n√\nn(log n)1+ε) and, surprisingly, the\nerror term is asymptotically normal, exhibiting an unexpected \ncentral limit theorem\nin St. Petersburg theory.", "subjects" : [ { "otype" : "Classification", "mtid" : 10003, "link" : "/api/classification/10003", "label" : "Matematika", "published" : true, "snippet" : true }, { "otype" : "Classification", "mtid" : 10029, "link" : "/api/classification/10029", "label" : "Statisztika és valószínűség (benne a statisztikai módszerek kutatása; nem tartalmazza az alkalmazott statisztikai módszereket, amik az adott szakterületek - gazdaságtudomány, szociológia, stb. - részeinek tekintendők.)", "published" : true, "snippet" : true } ], "fundings" : [ { "otype" : "Funding", "mtid" : 1971024, "link" : "/api/funding/1971024", "label" : "NKFIH(K 125569)", "published" : false, "oldId" : 1971024, "snippet" : true } ], "digital" : null, "printed" : null, "sourceYear" : 2018, "foreignEdition" : true, "foreignLanguage" : true, "fullPublication" : true, "conferencePublication" : false, "nationalOrigin" : true, "missingAuthor" : false, "oaType" : "GREEN", "oaTypeDisp" : "GREEN", "oaCheckDate" : "2024-02-19", "oaFree" : true, "oaLink" : "http://real.mtak.hu/83656", "citationCount" : 1, "citationCountUnpublished" : 0, "citationCountWoOther" : 1, "independentCitCountWoOther" : 1, "nationalOriginCitationCount" : 0, "foreignEditionCitationCount" : 1, "doiCitationCount" : 1, "wosCitationCount" : 1, "scopusCitationCount" : 0, "wosScopusCitationCount" : 1, "wosScopusCitationCountWoOther" : 1, "wosScopusIndependentCitationCount" : 1, "wosScopusIndependentCitationCountWoOther" : 1, "independentCitationCount" : 1, "selfCitationCount" : 0, "unhandledCitationCount" : 0, "citingPubCount" : 1, "independentCitingPubCount" : 1, "citingPubCountWoOther" : 1, "independentCitingPubCountWoOther" : 1, "unhandledCitingPubCount" : 0, "citedPubCount" : 5, "citedCount" : 5, "ratings" : [ { "otype" : "SjrRating", "mtid" : 10742085, "link" : "/api/sjrrating/10742085", "label" : "sjr:Q1 (2019) Scopus - Applied Mathematics STOCHASTIC PROCESSES AND THEIR APPLICATIONS 0304-4149", "listPos" : 76, "rankValue" : 0.24, "type" : "journal", "ratingType" : { "otype" : "RatingType", "mtid" : 10002, "link" : "/api/ratingtype/10002", "label" : "sjr", "code" : "sjr", "published" : true, "snippet" : true }, "subject" : { "otype" : "ClassificationExternal", "mtid" : 2604, "link" : "/api/classificationexternal/2604", "label" : "Scopus - Applied Mathematics", "published" : true, "oldId" : 2604, "snippet" : true }, "ranking" : "Q1", "calculation" : "DIRECT", "published" : true, "snippet" : true } ], "ratingsForSort" : "Q1", "hasCitationDuplums" : false, "userChangeableUntil" : "2019-01-31T22:59:00.000+0000", "publishDate" : "2018-09-12T10:26:29.000+0000", "directInstitutesForSort" : "Valószínűségszámítás és Statisztika (HRN RAMKI)", "ownerAuthorCount" : 1, "ownerInstituteCount" : 4, "directInstituteCount" : 1, "authorCount" : 1, "contributorCount" : 0, "hasQualityFactor" : true, "link" : "/api/publication/3414590", "label" : "István Berkes. 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