1-stable fluctuation of the derivative martingale of branching random walk

Haojie Hou; Yan Xia Ren; Renming Song

doi:10.1016/j.spa.2024.104338

1-stable fluctuation of the derivative martingale of branching random walk

Haojie Hou, Yan Xia Ren, Renming Song

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

Abstract

In this paper, we study the functional convergence in law of the fluctuations of the derivative martingale of branching random walk on the real line. Our main result strengthens the results of Buraczewski et al. (2021) and is the branching random walk counterpart of the main result of Maillard and Pain (2019) for branching Brownian motion.

Original language	English (US)
Article number	104338
Journal	Stochastic Processes and their Applications
Volume	172
DOIs	https://doi.org/10.1016/j.spa.2024.104338
State	Published - Jun 2024

Keywords

Branching random walk
Derivative martingale
Spine decomposition

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

Online availability

10.1016/j.spa.2024.104338

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title = "1-stable fluctuation of the derivative martingale of branching random walk",

abstract = "In this paper, we study the functional convergence in law of the fluctuations of the derivative martingale of branching random walk on the real line. Our main result strengthens the results of Buraczewski et al. (2021) and is the branching random walk counterpart of the main result of Maillard and Pain (2019) for branching Brownian motion.",

keywords = "Branching random walk, Derivative martingale, Spine decomposition",

author = "Haojie Hou and Ren, {Yan Xia} and Renming Song",

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language = "English (US)",

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T1 - 1-stable fluctuation of the derivative martingale of branching random walk

AU - Hou, Haojie

AU - Ren, Yan Xia

AU - Song, Renming

PY - 2024/6

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N2 - In this paper, we study the functional convergence in law of the fluctuations of the derivative martingale of branching random walk on the real line. Our main result strengthens the results of Buraczewski et al. (2021) and is the branching random walk counterpart of the main result of Maillard and Pain (2019) for branching Brownian motion.

AB - In this paper, we study the functional convergence in law of the fluctuations of the derivative martingale of branching random walk on the real line. Our main result strengthens the results of Buraczewski et al. (2021) and is the branching random walk counterpart of the main result of Maillard and Pain (2019) for branching Brownian motion.

KW - Branching random walk

KW - Derivative martingale

KW - Spine decomposition

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1-stable fluctuation of the derivative martingale of branching random walk

Abstract

Keywords

ASJC Scopus subject areas

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