Lindley-type equations in the branching random walk

被引：26
|
作者：
Biggins, JD
机构：
[1] Univ Sheffield, Dept Probabil & Stat, Sheffield S3 7RH, S Yorkshire, England
[2] Univ Minnesota, Inst Math & Applicat, Minneapolis, MN 55455 USA
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 1998年 / 75卷 / 01期
关键词：
maxima; extreme values; functional equations;
D O I：
10.1016/S0304-4149(98)00016-7
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
An analogue of the Lindley equation for random walk is studied in the context of the branching random walk, taking up the studies of Karpelevich, Kelbert and Suhov [(1993a) In: Boccara, N., Goles, E., Martinez, S., Picco, P. (Eds.), Cellular Automata and Cooperative Behaviour. Kluwer, Dordrecht, pp. 323-342; (1994a) Stochast. Process. Appl. 53, 65-96]. The main results are: (i) close to necessary conditions for the equation to have a solution, (ii) mild conditions for there to be a one-parameter family of solutions and (iii) mild conditions for this family to be the only possible solutions. (C) 1998 Elsevier Science B.V. All rights reserved.
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页码：105 / 133
页数：29
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