Survival of Branching Random Walks in Random Environment

被引：21

作者：

Gantert, Nina ^{[2
,3
]}

Mueller, Sebastian ^{[4
]}

Popov, Serguei ^{[1
]}

Vachkovskaia, Marina ^{[1
]}

机构：

[1] Univ Estadual Campinas, Inst Math Stat & Sci Computat, Dept Stat, BR-13083970 Campinas, SP, Brazil

[2] CeNos Ctr Nonlinear Sci, Fachbereich Math & Informat, D-48149 Munster, Germany

[3] Inst Stat Math, D-48149 Munster, Germany

[4] Graz Univ Technol, Inst Math Strukturtheorie, A-8010 Graz, Austria

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2010年 / 23卷 / 04期

基金：

巴西圣保罗研究基金会;

关键词：

Local extinction; Global extinction; Random matrices; Lyapunov exponent; LIMIT-THEOREMS; MATRICES; TREES;

D O I：

10.1007/s10959-009-0227-5

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：

We study survival of nearest-neighbor branching random walks in random environment (BRWRE) on Z. A priori there are three different regimes of survival: global survival, local survival, and strong local survival. We show that local and strong local survival regimes coincide for BRWRE and that they can be characterized with the spectral radius of the first moment matrix of the process. These results are generalizations of the classification of BRWRE in recurrent and transient regimes. Our main result is a characterization of global survival that is given in terms of Lyapunov exponents of an infinite product of i.i.d. 2x2 random matrices.

引用

页码：1002 / 1014

页数：13

共 20 条

[1]

[Anonymous], 2007, Lat. Am. J. Probab. Math. Statist.

[2]

BAILLON B, 1994, J REINE ANGEW MATH, V454, P181

[3]

Barbour AD, 1996, ANN APPL PROBAB, V6, P1045

[4] Characterization of Critical Values of Branching Random Walks on Weighted Graphs through Infinite-Type Branching Processes [J].

Bertacchi, Daniela ;

Zucca, Fabio .

JOURNAL OF STATISTICAL PHYSICS, 2009, 134 (01) :53-65

[5]

Bougerol P, 1985, PROGR PROBABILITY ST

[6] Multidimensional branching random walks in random environment [J].

Comets, Francis ;

Popov, Serguei .

ANNALS OF PROBABILITY, 2007, 35 (01) :68-114

[7]

Francis M, 1998, Markov Processes and Related Fields, V4, P465

[8]

GANTERT N, 2006, MARKOV PROCESS RELAT, V12, P805

[9] ON A VARIATIONAL PROBLEM FOR AN INFINITE PARTICLE SYSTEM IN A RANDOM MEDIUM .2. THE LOCAL GROWTH-RATE [J].

GREVEN, A ;

DENHOLLANDER, F .

PROBABILITY THEORY AND RELATED FIELDS, 1994, 100 (03) :301-328

[10] BRANCHING RANDOM-WALK IN RANDOM ENVIRONMENT - PHASE-TRANSITIONS FOR LOCAL AND GLOBAL GROWTH-RATES [J].

GREVEN, A ;

DENHOLLANDER, F .

PROBABILITY THEORY AND RELATED FIELDS, 1992, 91 (02) :195-249

← 1 2 →