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Families of birth-death processes with similar time-dependent behaviour

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

R. B. Lenin ,
P. R. Parthasarathy ,
W. R. W. Scheinhardt  and
E. A. van Doorn
R. B. Lenin*
Affiliation:
University of Antwerp
P. R. Parthasarathy*
Affiliation:
Indian Institute of Technology
W. R. W. Scheinhardt*
Affiliation:
Eindhoven University of Technology
E. A. van Doorn*
Affiliation:
University of Twente
*
∗Postal address: Department of Mathematics and Computer Science, University of Antwerp, Universiteitsplein 1, B-2610 Wilrijk, Belgium
∗∗Postal address: Department of Mathematics, Indian Institute of Technology, Madras, Chennai 600 036, India
∗∗∗Postal address: Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
∗∗∗∗Postal address: Faculty of Mathematical Sciences, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands. Email address: [email protected]
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Abstract

We consider birth-death processes taking values in but allow the death rate in state 0 to be positive, so that escape from is possible. Two such processes with transition functions are said to be similar if, for all there are constants cij such that for all t ≥ 0. We determine conditions on the birth and death rates of a birth-death process for the process to be a member of a family of similar processes, and we identify the members of such a family. These issues are also resolved in the more general setting in which the two processes are called similar if there are constants cij and ν such that for all t ≥ 0.

Keywords

Absorption probabilitychain sequenceinvariant vectortransient behaviourtransition function

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 3 , September 2000 , pp. 835 - 849
Copyright
Copyright © Applied Probability Trust 2000 

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