SPREADING SPEEDS IN REDUCIBLE MULTITYPE BRANCHING RANDOM WALK

被引：3

作者：

Biggins, J. D. ^{[1
]}

机构：

[1] Univ Sheffield, Sch Math & Stat, Sheffield S3 7RH, S Yorkshire, England

来源：

ANNALS OF APPLIED PROBABILITY | 2012年 / 22卷 / 05期

关键词：

Branching random walk; multitype; speed; anomalous spreading; reducible; PRESENCE PROBABILITIES; CONVEXITY PROPERTY;

D O I：

10.1214/11-AAP813

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：

This paper gives conditions for the rightmost particle in the nth generation of a multitype branching random walk to have a speed, in the sense that its location divided by n converges to a constant as n goes to infinity. Furthermore, a formula for the speed is obtained in terms of the reproduction laws. The case where the collection of types is irreducible was treated long ago. In addition, the asymptotic behavior of the number in the nth generation to the right of na is obtained. The initial motive for considering the reducible case Was results for a deterministic spatial population model with several types of individual discussed by Weinberger, Lewis and Li [J. Math. Biol. 55 (2007) 207-222]: the speed identified here for the branching random walk corresponds to an upper bound for the speed identified there for the deterministic model.

引用

页码：1778 / 1821

页数：44

共 20 条

[1]

[Anonymous], 1970, CONVEX ANAL

[2]

[Anonymous], 1973, Non-negative Matrices and Markov Chains

[3]

Asmussen S., 1983, Progress in Probability and Statistics, V3

[4] THE GROWTH AND SPREAD OF THE GENERAL BRANCHING RANDOM WALK [J].

Biggins, J. D. .

ANNALS OF APPLIED PROBABILITY, 1995, 5 (04) :1008-1024

[5]

BIGGINS J.D, 1976, THESIS U OXFORD

[6]

Biggins J. D., 1997, Classical and Modern Branching Processes: Proc. IMA Workshop, Minneapolis, P19, DOI DOI 10.1007/978-1-4612-1862-32

[7]

BIGGINS J. D., 2010, London Math. Soc. Lecture Note Ser., V378, P113

[8] Convergence results on multitype, multivariate branching random walks [J].

Biggins, JD ;

Sani, AR .

ADVANCES IN APPLIED PROBABILITY, 2005, 37 (03) :681-705

[9] 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

[10] CHERNOFFS THEOREM IN BRANCHING RANDOM-WALK [J].

BIGGINS, JD .

JOURNAL OF APPLIED PROBABILITY, 1977, 14 (03) :630-636

← 1 2 →