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

Published online by Cambridge University Press:  01 July 2016

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.

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.

Type
General Applied Probability
Copyright
Copyright © Applied Probability Trust 2003 

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