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.
引用
收藏
页码：105 / 133
页数：29
相关论文
共 20 条
[1]  
Asmussen S, 2008, APPL PROBABILITY QUE, V51
[2]   UNIFORM-CONVERGENCE OF MARTINGALES IN THE BRANCHING RANDOM-WALK [J].
BIGGINS, JD .
ANNALS OF PROBABILITY, 1992, 20 (01) :137-151
[3]   GROWTH-RATES IN THE BRANCHING RANDOM-WALK [J].
BIGGINS, JD .
ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1979, 48 (01) :17-34
[4]  
Biggins JD, 1997, ANN PROBAB, V25, P337
[5]   1ST-BIRTH AND LAST-BIRTH PROBLEMS FOR A MULTITYPE AGE-DEPENDENT BRANCHING-PROCESS [J].
BIGGINS, JD .
ADVANCES IN APPLIED PROBABILITY, 1976, 8 (03) :446-459
[6]   CHERNOFFS THEOREM IN BRANCHING RANDOM-WALK [J].
BIGGINS, JD .
JOURNAL OF APPLIED PROBABILITY, 1977, 14 (03) :630-636
[7]   MARTINGALE CONVERGENCE IN BRANCHING RANDOM-WALK [J].
BIGGINS, JD .
JOURNAL OF APPLIED PROBABILITY, 1977, 14 (01) :25-37
[8]  
BIGGINS JD, 1997, IMA VOL MATH APPL, V84, P19, DOI DOI 10.1007/978-1-4612-1862-3_2
[9]  
Bramson M., 1992, ANN APPL PROBAB, V2, P575
[10]  
Feller W., 1991, An Introduction to Probability Theory and Its Applications, VII
12