Extreme order statistics on Galton-Watson trees

被引:0
作者
Anthony G. Pakes
机构
[1] University of Western Australia,Department of Mathematics
来源
Metrika | 1998年 / 47卷
关键词
Branching Process; Order Statistics; Limit Theorems;
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摘要
This paper studies the asymptotic behaviour of extreme order statistics of i.i.d. random scores ascribed to each individual in a Galton-Watson family tree. Of interest is the asymptotic behaviour of the order statistics within thenth generation, or up to and including thenth generation, and the index of the generation up to thenth which contains the largest observation.
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页码:95 / 117
页数:22
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  • [1] Bingham NH(1974)Asymptotic properties of super-critical branching processes. I: The Galton-Watson process Adv. Appl. Prob. 6 711-731
  • [2] Doney RA(1992)I.J. Bienaymé: Family information and proof of the criticality theorem Intl. Statist. Review 60 177-183
  • [3] Bru B(1982)On a theorem of Bingham and Doney J. Appl. Prob. 19 217-220
  • [4] Jongmans F(1995)Three papers on the history of branching processes Intl. Statist. Review 63 233-245
  • [5] Seneta E(1971)Some limit theorems for the total progeny of a branching process Adv. Appl. Prob. 3 176-192
  • [6] de Meyer A(1983)Remarks on a model of competitive bidding for employment J. Appl. Prob. 20 349-357
  • [7] Guttorp P(1968)A lemma on the Galton-Watson process and some of its consequences Proc. Amer. Math. Soc. 19 1169-1179
  • [8] Pakes AG(1968)A branching process with mean one and possibly infinite variance Z. Wahrs. 9 139-145
  • [9] Pakes AG(1975)On the increasing distribution of the inter-record times in an increasing population J. Appl. Prob. 12 148-154
  • [10] Papangelou F(undefined)undefined undefined undefined undefined-undefined