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

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

Research output: Book/ReportReportProfessional

## 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 language Undefined Enschede University of Twente, Department of Applied Mathematics 14 0169-2690 Published - 1999

### Publication series

Name Memorandum / Department of Applied Mathematics Department of Applied Mathematics, University of Twente 1486 0169-2690

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