Abstract
Some theorems, which strengthen the asymptotic properties of the solutions of renewal equations, are proved. These results are applied in a study of the first two moments of age-dependent branching processes.
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W. Feller, “Fluctuation theory of recurrent events,” Trans. Am. Math. Soc.,67, 98–119 (1949).
D. Blackwell, “A renewal theorem,” Duke Math. J.,15, 145–150 (1948).
W. L. Smith, “Asymptotic renewal theorems,” Proc. Roy. Soc. Edinburgh,A64, 9–48 (1953–54).
W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 1. John Wiley and Sons, Inc., New York-London-Sydney (1960).
D. R. Cox, Renewal Theory. Methuen and Co., Ltd., London (1962).
D. V. Widder, The Laplace Transform. Princeton University Press, Princeton (1941).
I. M. Gel'fand, D. A. Raikov, and G. E. Shilov, Commutative Normed Rings [in Russian], Moscow (1960).
B. A. Sevast'yanov, “Branching processes with conversions depending on the age of the particles,” Teoriya Veroyat. i ee Primen.,9, No. 4, 577–594 (1964).
T. E. Harris, The Theory of Branching Processes [Russian translation], Moscow (1966).
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Translated from Matematicheskie Zametki, Vol. 3, No. 1, pp. 3–14, January, 1968.
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Sevast'yanov, B.A. Renewal equations and moments of branching processes. Mathematical Notes of the Academy of Sciences of the USSR 3, 3–10 (1968). https://doi.org/10.1007/BF01386956
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DOI: https://doi.org/10.1007/BF01386956