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Linear birth and death processes with killing

Published online by Cambridge University Press:  14 July 2016

Samuel Karlin  and
Simon Tavaré
Samuel Karlin*
Affiliation:
Stanford University
Simon Tavaré*
Affiliation:
Colorado State University
*
∗Postal address: Department of Mathematics, Stanford University, Stanford, CA 94305, U.S.A.
∗∗Postal address: Department of Statistics, Colorado State University, Fort Collins, CO 80523, U.S.A.
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Abstract

We analyze a class of linear birth and death processes X(t) with killing. The generator is of the form λ i = bi + θ, µi = ai, γ i = ci, where γ i is the killing rate. Then P{killed in (t, t + h) | X(t) = i} = γ ih + o(h), h ↓ 0. A variety of explicit results are found, and an example from population genetics is given.

Keywords

BIRTH-DEATH PROCESSESKILLINGPOPULATION GENETICS
Type
Research Papers
Information
Journal of Applied Probability , Volume 19 , Issue 3 , September 1982 , pp. 477 - 487
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

Research supported in part by NIH Grant 5R01 GM10452–18 and NSF Grant MCS-24310.

References

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