THE GROWTH AND SPREAD OF THE GENERAL BRANCHING RANDOM WALK

被引：32

作者：

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

机构：

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

来源：

ANNALS OF APPLIED PROBABILITY | 1995年 / 5卷 / 04期

关键词：

Spatial spread; asymptotic speed; propagation rate; CMJ process;

D O I：

10.1214/aoap/1177004604

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：

A general (Crump-Mode-Jagers) spatial branching process is considered. The asymptotic behavior of the numbers present at time t in sets of the form [ta, infinity) is obtained. As a consequence it is shown that if B-t is the position of the rightmost person at time t, B-t/t converges to a constant, which can be obtained from the individual reproduction law, almost surely on the survival set of the process. This generalizes the known discrete-time results.

引用

页码：1008 / 1024

页数：17

共 13 条

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

BIGGINS, JD .

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

[2]

BIGGINS JD, 1980, LECT NOTES BIOMATH, V38, P57

[3] A MARTINGALE APPROACH TO SUPERCRITICAL (CMJ) BRANCHING-PROCESSES [J].

COHN, H .

ANNALS OF PROBABILITY, 1985, 13 (04) :1179-1191

[4]

DEVROYE L, 1990, RANDOM STRUCT ALGOR, V1, P191, DOI DOI 10.1002/RSA.3240010206

[5] LARGE DEVIATIONS FOR A GENERAL-CLASS OF RANDOM VECTORS [J].

ELLIS, RS .

ANNALS OF PROBABILITY, 1984, 12 (01) :1-12

[6]

GARTNER J, 1977, THEOR PROBAB APPL+, V22, P24

[7] GENERAL BRANCHING-PROCESSES AS MARKOV-FIELDS [J].

JAGERS, P .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1989, 32 (02) :183-212

[8]

JAGERS P, 1975, BRANCHING PROCESSES

[9] ON THE CONVERGENCE OF SUPERCRITICAL GENERAL (C-M-J) BRANCHING-PROCESSES [J].

NERMAN, O .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1981, 57 (03) :365-395

[10]

Rockafellar R.T., 1970, CONVEX ANAL, V2nd

← 1 2 →