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

R.B. Lenin, P.R. Parthasarathy, W.R.W. Scheinhardt, E.A. van Doorn

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We consider birth-death processes taking values in ${\cal N} \equiv \{0,1,\ldots\}$, but allow the death rate in state $0$ to be positive, so that escape from ${\cal N}$ is possible. Two such processes with transition functions $\{p_{ij}(t)\}$ and $\{{\tilde p}_{ij}(t)\}$ are said to be {\it similar} if, for all $i,j \in {\cal N},$ there are constants $c_{ij}$ such that ${\tilde p}_{ij}(t) = c_{ij}p_{ij}(t)$ for all $t \geq 0.$ 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.
Original languageEnglish
Place of PublicationEnschede
PublisherUniversity of Twente
Number of pages14
Publication statusPublished - 1999

Publication series

PublisherDepartment of Applied Mathematics, University of Twente
ISSN (Print)0169-2690


  • MSC-60J80


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