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Some Problems in Mathematical Genealogy

Published online by Cambridge University Press:  05 September 2017

David G. Kendall
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Abstract

After a general review of symmetric reversibility for countable-state continuous-time Markov chains the author shows that the birth-death-and-immigration process is symmetrically reversible and further that it remains so even when the description of the present state is refined to include a list of the sizes of all ‘families’ alive at the epoch in question. This result can be useful in genealogy because the operational direction of time there is the negative one. In view of the symmetric reversibility, some of the questions which face the genealogist can be answered without further calculation by quoting known results for the process with the usual (‘forward’ instead of ‘backward’) direction of time.

Further topics discussed include social mobility matrices, surname statistics, and Colin Rogers' ‘problem of the Spruces’.

Type
Part VIII — Probability Models in the Humanities
Information
Journal of Applied Probability , Volume 12 , Issue S1 , 1975 , pp. 325 - 345
Copyright
Copyright © 1975 Applied Probability Trust 

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References

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