Convergence of complex martingale for a branching random walk in a time random environment

Xiaoqiang Wang; Chunmao Huang

doi:10.1214/19-ECP247

Convergence of complex martingale for a branching random walk in a time random environment

Xiaoqiang Wang
, Chunmao Huang^*

^*Corresponding author for this work

Shandong University
Harbin Institute of Technology Weihai

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

7 Scopus citations

Abstract

We consider a discrete-time branching random walk in a stationary and ergodic environment ξ = (ξ_n) indexed by time n ∈ N. Let W_n(z) (z ∈ C^d) be the natural complex martingale of the process. We show sufficient conditions for its almost sure and quenched Lα convergence, as well as the existence of quenched moments and weighted moments of its limit, and also describe the exponential convergence rate.

Original language	English
Article number	41
Journal	Electronic Communications in Probability
Volume	24
DOIs	https://doi.org/10.1214/19-ECP247
State	Published - 2019
Externally published	Yes

Keywords

Branching random walk
Complex martingale
Convergence rate
Moments
Random environment
Weighted moments

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10.1214/19-ECP247

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abstract = "We consider a discrete-time branching random walk in a stationary and ergodic environment ξ = (ξn) indexed by time n ∈ N. Let Wn(z) (z ∈ Cd) be the natural complex martingale of the process. We show sufficient conditions for its almost sure and quenched Lα convergence, as well as the existence of quenched moments and weighted moments of its limit, and also describe the exponential convergence rate.",

keywords = "Branching random walk, Complex martingale, Convergence rate, Moments, Random environment, Weighted moments",

author = "Xiaoqiang Wang and Chunmao Huang",

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AU - Huang, Chunmao

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N2 - We consider a discrete-time branching random walk in a stationary and ergodic environment ξ = (ξn) indexed by time n ∈ N. Let Wn(z) (z ∈ Cd) be the natural complex martingale of the process. We show sufficient conditions for its almost sure and quenched Lα convergence, as well as the existence of quenched moments and weighted moments of its limit, and also describe the exponential convergence rate.

AB - We consider a discrete-time branching random walk in a stationary and ergodic environment ξ = (ξn) indexed by time n ∈ N. Let Wn(z) (z ∈ Cd) be the natural complex martingale of the process. We show sufficient conditions for its almost sure and quenched Lα convergence, as well as the existence of quenched moments and weighted moments of its limit, and also describe the exponential convergence rate.

KW - Branching random walk

KW - Complex martingale

KW - Convergence rate

KW - Moments

KW - Random environment

KW - Weighted moments

UR - https://www.scopus.com/pages/publications/85071294330

U2 - 10.1214/19-ECP247

DO - 10.1214/19-ECP247

M3 - 文章

AN - SCOPUS:85071294330

SN - 1083-589X

VL - 24

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

M1 - 41

ER -

Convergence of complex martingale for a branching random walk in a time random environment

Abstract

Keywords

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