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

  • R. B. Lenin (a1), P. R. Parthasarathy (a2), W. R. W. Scheinhardt (a3) and E. A. van Doorn (a4)


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 c ij 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 c ij and ν such that for all t ≥ 0.


Corresponding author

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:


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