Birth-death processes on trees
type: Item
instance of: scholarly article
title: Birth-death processes on trees
zbMATH Open document ID: 1213.37013
published in: Science China. Mathematics
publication date: 2011-02-25T00:00:00Z
review text: This paper develops earlier work of \textit{S. Yan} and \textit{M. Chen} [Chin. Ann. Math., Ser. B 7, 90--110 (1986; Zbl 0596.60074)] and \textit{B. Wu} and \textit{Y.-H. Zhang} [J. Appl. Prob. 44, No. 1, 226--237 (2007; Zbl 1133.60345)] in the setting of the positive integers to study some birth-death processes on trees. The lack of a total order restricts what can be done, and here two different birth-death processes are constructed for which computable criteria can be found for recurrence, ergodicity, and other attributes. Upper and lower bounds are found for the Dirichlet eigenvalue.
reviewed by: Thomas B. Ward
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 37A50
zbMATH DE Number: 5857733
zbMATH Keywords: random walk
zbMATH Keywords: tree
zbMATH Keywords: recurrent
zbMATH Keywords: ergodic
author: Yutao Ma
MaRDI profile type: Publication
full work available at URL: s11425-010-4077-5
OpenAlex ID: W2036418461
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DOI: 10.1007/S11425-010-4077-5
description: scientific article; zbMATH DE number 5857733