Abstract: We study a critical branching random walk on a real line with discrete time controlled by a point process. Sizes of sequential generations form Galton–Watson critical process with one type of particles. The particle coordinates are interpreted as the weights of the vertices on the genealogical tree of the random walk. A reduced tree is obtained after removing branches of the genealogical tree that do not reach the n-th level. The asymptotic behavior of the first two moments of the number of vertices and of the sum of vertex weights over all levels of reduced tree under condition of nonextinction is described. Several limit theorems for the weights of particles in a branching random walk up to n-th generation under condition of nonextinction are proved.

Cite: Topchii V.A.
Properties of critical branching random walks on the line under non-extinction condition
Discrete Mathematics and Applications. 2025. V.35. N3. P.187-202. DOI: 10.1515/dma-2025-0014 WOS Scopus OpenAlex

Original: Топчий В.А.
Свойства критических ветвящихся случайных блужданий на прямой при условии невырождения
Дискретная математика. 2023. Т.35. №1. С.107-127. DOI: 10.4213/dm1709 РИНЦ OpenAlex

Dates:

Submitted:	Apr 18, 2022
Accepted:	Oct 29, 2022
Published print:	Jun 26, 2025
Published online:	Jul 25, 2025

Identifiers:

Web of science:	WOS:001529353200003
Scopus:	2-s2.0-105011083143
OpenAlex:	W4412433076

Citing: Пока нет цитирований

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