@book{9832cb234bfe4ec18da07d03775d59c7,

title = "Families of birth-death processes with similar time-dependent behaviour",

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.",

keywords = "EWI-3306, IR-65675, METIS-141298, MSC-60J80",

author = "R.B. Lenin and P.R. Parthasarathy and Scheinhardt, {Willem R.W.} and {van Doorn}, {Erik A.}",

note = "Imported from MEMORANDA",

year = "1999",

language = "Undefined",

isbn = "0169-2690",

series = "Memorandum / Department of Applied Mathematics",

publisher = "University of Twente, Department of Applied Mathematics",

number = "1486",

}