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On age dependent branching processes

Published online by Cambridge University Press:  14 July 2016

Howard Weiner*
Affiliation:
University of California, Davis

Extract

This paper deals with asymptotic properties of various models of age dependent branching processes, relying heavily on Harris [3].

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 

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References

[1] Bellman, R. and Cooke, K. L. (1963) Differential-Difference Equations. Academic Press, New York.Google Scholar
[2] Chung, K. L. (1960) Markov Chains with Stationary Transition Probabilities. Springer, Berlin.Google Scholar
[3] Harris, T. E. (1963) The Theory of Branching Processes. Springer, Berlin, and Prentice Hall, New Jersey.Google Scholar
[4] Kendall, D. G. (1948) On a generalized ‘birth-and-death’ process. Ann. Math. Statist. 19, 115.CrossRefGoogle Scholar
[5] Kendall, D. G. (1952) Les processus stochastiques de croissance en biologie. Ann. Inst. Poincaré, 13, 43108.Google Scholar
[6] Kendall, D. G. (1949) Stochastic processes and population growth. J. R. Statist. Soc. B, 11, 230264.Google Scholar
[7] Smith, W. L. (1955) Regenerative stochastic processes. Proc. R. Statist. Soc. A. 232, 631.Google Scholar
[8] Snow, R. N. (1959) N-dimensional age dependent branching processes—asymptotic behavior, irreducible case. Amer. Math. Soc. Notices 6, No. 6, 616617 (abstract).Google Scholar
[9] Stohlman, F. Jr., (ed) (1959) The Kinetics of Cellular Proliferation. Grune and Stratton, New York.Google Scholar
[10] Weiner, H. J. (1966) Applications of the age distribution in age dependent branching processes. J. Appl. Prob. 3, 179201.Google Scholar
[11] Weiner, H. J. (1966) Asymptotic properties of an age dependent branching process. Ann. Math. Statist. (to appear).Google Scholar
[12] Widder, D. V. (1946) The Laplace Transform. Princeton University Press, Princeton.Google Scholar