The first Dirichlet eigenvalue of birth–death process on trees

Ling-Di Wang and Yu-Hui Zhang

Statistics & Probability Letters, 2013, vol. 83, issue 9, 1973-1982

Abstract: This paper investigates the birth–death (“B–D” for short) process on trees, emphasizing on estimating the principal eigenvalue (equivalently, the convergence rate) of the process with Dirichlet boundary at the unique root 0. Three kinds of variational formulas for the eigenvalue are presented. As an application, we obtain a criterion for positivity of the first eigenvalue for B–D processes on trees with one branch after some layer.

Keywords: Dirichlet eigenvalue; Variational formula; Birth–death process on tree (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.spl.2013.05.001

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