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The λ-classification of continuous-time birth-and-death processes

Part of: Markov processes

Published online by Cambridge University Press:  01 July 2016

Andrew G. Hart ,
Servet Martínez  and
Jaime San Martín
Andrew G. Hart*
Affiliation:
Universidad de Chile, Santiago
Servet Martínez*
Affiliation:
Universidad de Chile, Santiago
Jaime San Martín*
Affiliation:
Universidad de Chile, Santiago
*
∗ Postal address: Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, UMR 2071 CNRS-UCHILE, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 170-3, Correo 3, Santiago, Chile.
∗ Postal address: Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, UMR 2071 CNRS-UCHILE, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 170-3, Correo 3, Santiago, Chile.
∗ Postal address: Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, UMR 2071 CNRS-UCHILE, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 170-3, Correo 3, Santiago, Chile.
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Abstract

We study the λ-classification of absorbing birth-and-death processes, giving necessary and sufficient conditions for such processes to be λ-transient, λ-null recurrent and λ-positive recurrent.

Keywords

Birth-and-death processdecay parameterλ-theoryabsorptionnonexplosivity

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 35 , Issue 4 , December 2003 , pp. 1111 - 1130
Copyright
Copyright © Applied Probability Trust 2003 

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