Ratio limit theorems for cascade processes

  • P. E. Ney
Article

Keywords

Stochastic Process Probability Theory Limit Theorem Mathematical Biology Cascade Process 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Bellman, R., and T. E. Harris: On age-dependent binary branching processes. Ann. of Math. 55, 280–295 (1952).Google Scholar
  2. [2]
    Bharucha-Reid, A. T.: Elements of the Theory of Markov Processes and their Applications. New York: McGraw-Hill 1960.Google Scholar
  3. [3]
    Feller, W.: On the integral equation of renewal theory. Ann. math. Statistics 19, 474–494 (1941).Google Scholar
  4. [4]
    Harris, T. E.: Branching processes. Ann. math. Statistics 19, 474–494 (1948).Google Scholar
  5. [5]
    - Some mathematical models for branching processes. Proc. 2nd Berckley Sympos. math. Statistics Probability 305–328 (1951).Google Scholar
  6. [6]
    Janossy, L.: Note on the fluctuation problem of cascades. Proc. phys. Soc. (London), Sect. A, 34, 241–249 (1950).Google Scholar
  7. [7]
    Levinson, N.: Limiting theorems for age-dependent branching processes. Illinois J. Math. 4, 100–118 (1960).Google Scholar
  8. [8]
    Lopuszanski, J.: Some remarks on the asymptotic behavior of the cosmic ray cascade for large depth of the absorber: II. Asymptotic behavior of the probability distribution function, Nuovo Cimento, X Ser. 2, Suppl. 4, 1150–1160 (1955).Google Scholar
  9. [9]
    —: Some remarks on the asymptotic behavior of the cosmic ray cascade for large depth of the absorber: III. Evaluation of the distribution function, Nuovo Cimento, X. Ser. 2, Suppl. 4, 1161–1167 (1955).Google Scholar
  10. [10]
    Ney, P. E.: Generalized branching processes I: Existence and uniqueness theorems. To appear in Illinois J. Math. (1964).Google Scholar
  11. [11]
    Ney, P.E.: Generalized branching processes II: Asymptotic theory. To appear in Illinois J. Math. (1964).Google Scholar
  12. [12]
    —: The limit of a ratio of convolutions. Ann. math. Statistics 34, 457–461 (1963).Google Scholar
  13. [13]
    Urbanik, K.: Some remarks on the asymptotic behavior of the cosmic ray cascade for large depth of the absorber: I. Evaluation of the factorial moments. Nuovo Cimento, X. Ser. 2, Suppl. 4, 1147–1149 (1955).Google Scholar

Copyright information

© Springer-Verlag 1964

Authors and Affiliations

  • P. E. Ney
    • 1
  1. 1.Cornell University IthacaNew YorkUSA

Personalised recommendations