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

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

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Abstract

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 languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages14
ISBN (Print)0169-2690
Publication statusPublished - 1999

Publication series

NameMemorandum / Department of Applied Mathematics
PublisherDepartment of Applied Mathematics, University of Twente
No.1486
ISSN (Print)0169-2690

Keywords

  • EWI-3306
  • IR-65675
  • METIS-141298
  • MSC-60J80

Cite this

Lenin, R. B., Parthasarathy, P. R., Scheinhardt, W. R. W., & van Doorn, E. A. (1999). Families of birth-death processes with similar time-dependent behaviour. (Memorandum / Department of Applied Mathematics; No. 1486). Enschede: University of Twente, Department of Applied Mathematics.