Limit Theorems for the Minimal Position of a Branching Random Walk in Random Environment

被引：0

作者：

Zhang, Xiaoyue ^{[1
]}

Hou, Wanting ^{[2
]}

Hong, Wenming ^{[3
,4
]}

机构：

[1] Capital Univ Econ & Business, Sch Stat, Beijing 100070, Peoples R China

[2] Northeastern Univ, Dept Math, Shenyang 110004, Peoples R China

[3] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

[4] Beijing Normal Univ, Lab Math & Complex Syst, Beijing 100875, Peoples R China

来源：

MARKOV PROCESSES AND RELATED FIELDS | 2020年 / 26卷 / 05期

关键词：

random walk in random environment; branching random walk; branching process; minimal position; DISPLACEMENT; SYSTEM;

D O I：

暂无

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 consider a branching system of N-valued random walks with a random environment in location. We will give the exact limit value of M-n/n, where M-n denotes the minimal position of the branching random walk at time n. A key step in the proof is to transfer our branching random walks with a random environment in location to branching random walks with a random environment in time, by use of Bramson's "branching processes within a branching process" (1978).

引用

页码：839 / 860

页数：22

共 50 条

[21] Limit theorems for a supercritical branching process with immigration in a random environment
YanQing Wang
QuanSheng Liu
[J]. Science China Mathematics, 2017, 60 : 2481 - 2502
[22] Limit theorems for a supercritical branching process with immigration in a random environment
WANG YanQing
LIU QuanSheng
[J]. Science China Mathematics, 2017, 60 (12) : 2481 - 2502
[23] Limit Theorems for Weakly Subcritical Branching Processes in Random Environment
Afanasyev, V. I.
Boeinghoff, C.
Kersting, G.
Vatutin, V. A.
[J]. JOURNAL OF THEORETICAL PROBABILITY, 2012, 25 (03) : 703 - 732
[24] Limit theorems for a supercritical branching process with immigration in a random environment
Wang, YanQing
Liu, QuanSheng
[J]. SCIENCE CHINA-MATHEMATICS, 2017, 60 (12) : 2481 - 2502
[25] Limit Theorems for Weakly Subcritical Branching Processes in Random Environment
V. I. Afanasyev
C. Böinghoff
G. Kersting
V. A. Vatutin
[J]. Journal of Theoretical Probability, 2012, 25 : 703 - 732
[26] LIMIT-THEOREMS FOR BRANCHING-PROCESSES IN A RANDOM ENVIRONMENT
TANNY, D
[J]. ANNALS OF PROBABILITY, 1977, 5 (01): : 100 - 116
[27] MINIMAL POSITIONS IN A BRANCHING RANDOM WALK
McDiarmid, Colin
[J]. ANNALS OF APPLIED PROBABILITY, 1995, 5 (01): : 128 - 139
[28] The limit theorems for random walk with state space ℝ in a space-time random environment
Wei Gang Wang
Zhen Long Gao
Di He Hu
[J]. Acta Mathematica Sinica, English Series, 2008, 24 : 655 - 662
[29] Limit Theorems for the ‘Laziest’ Minimal Random Walk Model of Elephant Type
Tatsuya Miyazaki
Masato Takei
[J]. Journal of Statistical Physics, 2020, 181 : 587 - 602
[30] LIMIT THEOREMS FOR AN ASYMMETRIC RANDOM WALK
MIKLUKHI.OG
[J]. THEORY OF PROBILITY AND ITS APPLICATIONS,USSR, 1970, 15 (04): : 710 - &

← 1 2 3 4 5 →