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


Lenin, R.B. and Parthasarathy, P.R. and Scheinhardt, W.R.W. and Doorn, E.A. van (2000) Families of birth-death processes with similar time-dependent behaviour. Journal of Applied Probability, 37 (3). pp. 835-849. ISSN 0021-9002

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Abstract:We consider birth-death processes taking values in N ≡ {0,1,... }, but allow the death rate in state 0 to be positive, so that escape from N is possible. Two such processes with transition functions { pij(t) } and { ̃pij(t) } are said to be similar if, for all i, j ∈ N, there are constants cij such that ̃pij(t) = cijpij(t) 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 cij and ν such that ̃pij(t) = cijeνtpij(t) for all t ≥ 0.
Item Type:Article
Copyright:© 2000 Applied Probability Trust
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/62348
Official URL:https://doi.org/10.1239/jap/1014842840
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