Convergence of Martingale and Moderate Deviations for a Branching Random Walk with a Random Environment in Time

Xiaoqiang Wang; Chunmao Huang

doi:10.1007/s10959-016-0668-6

Convergence of Martingale and Moderate Deviations for a Branching Random Walk with a Random Environment in Time

Xiaoqiang Wang
, Chunmao Huang^*

^*Corresponding author for this work

Shandong University
Harbin Institute of Technology Weihai

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We consider a branching random walk on R with a stationary and ergodic environment ξ= (ξ_n) indexed by time n∈ N. Let Z_n be the counting measure of particles of generation n and Z~ _n(t) = ∫ e ^t ^xZ_n(d x) be its Laplace transform. We show the L^p convergence rate and the uniform convergence of the martingale Z~ _n(t) / E[ Z~ _n(t) | ξ] , and establish a moderate deviation principle for the measures Z_n.

Original language	English
Pages (from-to)	961-995
Number of pages	35
Journal	Journal of Theoretical Probability
Volume	30
Issue number	3
DOIs	https://doi.org/10.1007/s10959-016-0668-6
State	Published - 1 Sep 2017
Externally published	Yes

Keywords

Branching random walk
Convergence rate
L convergence
Moderate deviation
Moment
Random environment
Uniform convergence

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10.1007/s10959-016-0668-6

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title = "Convergence of Martingale and Moderate Deviations for a Branching Random Walk with a Random Environment in Time",

abstract = "We consider a branching random walk on R with a stationary and ergodic environment ξ= (ξn) indexed by time n∈ N. Let Zn be the counting measure of particles of generation n and Z\textasciitilde{} n(t) = ∫ e t xZn(d x) be its Laplace transform. We show the Lp convergence rate and the uniform convergence of the martingale Z\textasciitilde{} n(t) / E[ Z\textasciitilde{} n(t) | ξ] , and establish a moderate deviation principle for the measures Zn.",

keywords = "Branching random walk, Convergence rate, L convergence, Moderate deviation, Moment, Random environment, Uniform convergence",

author = "Xiaoqiang Wang and Chunmao Huang",

note = "Publisher Copyright: {\textcopyright} 2016, Springer Science+Business Media New York.",

year = "2017",

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TY - JOUR

T1 - Convergence of Martingale and Moderate Deviations for a Branching Random Walk with a Random Environment in Time

AU - Wang, Xiaoqiang

AU - Huang, Chunmao

PY - 2017/9/1

Y1 - 2017/9/1

N2 - We consider a branching random walk on R with a stationary and ergodic environment ξ= (ξn) indexed by time n∈ N. Let Zn be the counting measure of particles of generation n and Z~ n(t) = ∫ e t xZn(d x) be its Laplace transform. We show the Lp convergence rate and the uniform convergence of the martingale Z~ n(t) / E[ Z~ n(t) | ξ] , and establish a moderate deviation principle for the measures Zn.

AB - We consider a branching random walk on R with a stationary and ergodic environment ξ= (ξn) indexed by time n∈ N. Let Zn be the counting measure of particles of generation n and Z~ n(t) = ∫ e t xZn(d x) be its Laplace transform. We show the Lp convergence rate and the uniform convergence of the martingale Z~ n(t) / E[ Z~ n(t) | ξ] , and establish a moderate deviation principle for the measures Zn.

KW - Branching random walk

KW - Convergence rate

KW - L convergence

KW - Moderate deviation

KW - Moment

KW - Random environment

KW - Uniform convergence

UR - https://www.scopus.com/pages/publications/84955238872

U2 - 10.1007/s10959-016-0668-6

DO - 10.1007/s10959-016-0668-6

M3 - 文章

AN - SCOPUS:84955238872

SN - 0894-9840

VL - 30

SP - 961

EP - 995

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

IS - 3

ER -

Convergence of Martingale and Moderate Deviations for a Branching Random Walk with a Random Environment in Time

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Keywords

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