Critical survival barrier for branching random walk

被引：1

作者：

Liu, Jingning ^{[1
]}

Zhang, Mei ^{[1
,2
]}

机构：

[1] Chongqing Normal Univ, Sch Math Sciences, Chongqing, Peoples R China

[2] Beijing Normal Univ, Sch Math Sciences, Lab Math, Complex Syst, Beijing, Beijing, Peoples R China

来源：

FRONTIERS OF MATHEMATICS IN CHINA | 2019年 / 14卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Branching random walk; alpha-stable spine; absorption; critical barrier;

D O I：

10.1007/s11464-019-0806-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a branching random walk with an absorbing barrier, where the associated one-dimensional random walk is in the domain of attraction of an alpha-stable law. We shall prove that there is a barrier and a critical value such that the process dies under the critical barrier, and survives above it. This generalizes previous result in the case that the associated random walk has finite variance.

引用

页码：1259 / 1280

页数：22

共 50 条

[1] Critical survival barrier for branching random walk
Jingning Liu
Mei Zhang
Frontiers of Mathematics in China, 2019, 14 : 1259 - 1280
[2] The critical barrier for the survival of branching random walk with absorption
Jaffuel, Bruno
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2012, 48 (04): : 989 - 1009
[3] Asymptotic behavior of survival probability for a branching random walk with a barrier
Lv, You
AIMS MATHEMATICS, 2023, 8 (02): : 5049 - 5059
[4] Branching random walk with a critical branching part
Kesten, H
JOURNAL OF THEORETICAL PROBABILITY, 1995, 8 (04) : 921 - 962
[5] On the maximal displacement of critical branching random walk
Steven P. Lalley
Yuan Shao
Probability Theory and Related Fields, 2015, 162 : 71 - 96
[6] Branching random walk with selection at critical rate
Mallein, Bastien
BERNOULLI, 2017, 23 (03) : 1784 - 1821
[7] Critical branching random walk in an IID environment
Englaender, Janos
Sieben, Nandor
MONTE CARLO METHODS AND APPLICATIONS, 2011, 17 (02) : 169 - 193
[8] On the maximal displacement of critical branching random walk
Lalley, Steven P.
Shao, Yuan
PROBABILITY THEORY AND RELATED FIELDS, 2015, 162 (1-2) : 71 - 96
[9] The near-critical Gibbs measure of the branching random walk
Pain, Michel
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2018, 54 (03): : 1622 - 1666
[10] First order transition for the branching random walk at the critical parameter
Madaule, Thomas
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2016, 126 (02) : 470 - 502

← 1 2 3 4 5 →