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Poisson convergence on continuous time Branching Random Walks and multistage carcinogenesis

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Abstract

A theorem for Poisson convergence on realizations of twodimensional Branching Random Walks with an underlying continuous time Markov Branching Process is proved. This result can be used to gain an approximation for the number of cells having sustained a certain deficiency after a long time in multistage carcinogenesis.

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References

  1. Athreya, K. B., Ney, P. E.: Branching processes. Berlin-Heidelberg-New York: Springer 1972

    Google Scholar 

  2. Bahr, B. von, Esseen, C.-G.: Inequalities for the rth absolute moment of a sum of random variables, 1 ⩽ r ⩽ 2. Ann. Math. Statist. 36, 299–303 (1965)

    Google Scholar 

  3. Bühler, W. J., Lenz, N.: Chemical carcinogenesis and clonal selection. To appear in Proc. of the Conf. on Statistics and Cancer, Berkeley, July 6–7, 1981, edited by J. Neyman and L. Le Cam. Amsterdam: North Holland Publication Co.

    Google Scholar 

  4. Chiang, C. L.: The theory of multi-stage carcinogenesis. Submitted for publication to Bull. Math. Biol.

  5. Moncayo, A. R.: Poisson convergence and family trees. Ann. Prob. 3, No. 6, 1059–1061 (1975)

    Google Scholar 

  6. Neyman, J., Scott, E. L.: Statistical aspect of the problem of carcinogenesis. Proc. of the Fifth Berkeley Symp. on Math., Statist. and Prob., Univ. of Calif. Press 4, 745–776 (1967)

    Google Scholar 

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Lenz, N. Poisson convergence on continuous time Branching Random Walks and multistage carcinogenesis. J. Math. Biology 14, 301–307 (1982). https://doi.org/10.1007/BF00275395

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  • DOI: https://doi.org/10.1007/BF00275395

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