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The limiting behavior of transient birth and death processes conditioned on survival

Published online by Cambridge University Press:  09 April 2009

Phillip Good
Phillip Good
Affiliation:
Information Research Associates, Inc. San Diego, Calif.
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The development of a population over time can often be simulated by the behavior of a birth and death process, whose transition probability matrix P(t) = (Pij(t), where X(t) denotes the number of individuals at time t, satisfies the differential equations and the initial condition

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 8 , Issue 4 , November 1968 , pp. 716 - 722
Copyright
Copyright © Australian Mathematical Society 1968

References

[1]Good, P., (1965), ‘Limiting Conditional Behavior of Some Transient Chains’, doctoral dissertation, University of California, Berkeley.Google Scholar
[2]Karlin, S. and McGregor, J. (1957a) ‘Differential Equations of Birth and Death Process and the Stieltjes Moment Problem’, Trans. American Math. Soc. 85, 489.CrossRefGoogle Scholar
[3]Karlin, S. and McGregor, J. (1957b) ‘The Classification of Birth and Death Processes’, Trans. American Math. Soc. 86, 366.CrossRefGoogle Scholar
[4]Hodges, J. L. and Rosenblatt, M. (1953) ‘Recurrence-time Moments in Random Walks’, Pacific J. Math. 3, 127–136.CrossRefGoogle Scholar