The Annals of Probability

T. E. Harris and branching processes

K. B. Athreya and P. E. Ney

Full-text: Open access

Abstract

T. E. Harris was a pioneer par excellence in many fields of probability theory. In this paper, we give a brief survey of the many fundamental contributions of Harris to the theory of branching processes, starting with his doctoral work at Princeton in the late forties and culminating in his fundamental book “The Theory of Branching Processes,” published in 1963.

Article information

Source
Ann. Probab., Volume 39, Number 2 (2011), 429-434.

Dates
First available in Project Euclid: 25 February 2011

Permanent link to this document
https://projecteuclid.org/euclid.aop/1298669168

Digital Object Identifier
doi:10.1214/10-AOP599

Mathematical Reviews number (MathSciNet)
MR2789502

Zentralblatt MATH identifier
1213.60132

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
Branching processes

Citation

Athreya, K. B.; Ney, P. E. T. E. Harris and branching processes. Ann. Probab. 39 (2011), no. 2, 429--434. doi:10.1214/10-AOP599. https://projecteuclid.org/euclid.aop/1298669168


Export citation

References

  • [1] Athreya, K. B. and Ney, P. E. (1972). Branching Processes. Springer, New York.
  • [2] Bartlett, M. S. and Kendall, D. G. (1951). On the use of the characteristic functional in the analysis of some stochastic processes occurring in physics and biology. Proc. Cambridge Philos. Soc. 47 65–76.
  • [3] Bellman, R. and Harris, T. E. (1948). Age-dependent stochastic branching processes. Proc. Natl. Acad. Sci. USA 34 601–604.
  • [4] Bhabha, H. J. and Heitler, W. (1937). The passage of fast electrons and the theory of cosmic showers. Proc. Roy. Soc. London Ser. A 159 432–458.
  • [5] Harris, T. E. (1963). The Theory of Branching Processes. Die Grundlehren der Mathematischen Wissenschaften 119. Springer, Berlin.
  • [6] Harris, T. E. (1948). Branching processes. Ann. Math. Statist. 19 474–494.
  • [7] Harris, T. E. (1951). Some mathematical models for branching processes. In Proc. Second Berkeley Sympos. Math. Statist. Probab. 1950 305–328. Univ. California Press, Berkeley, CA.
  • [8] Harris, T. E. (1957). The random functions of cosmic-ray cascades. Proc. Natl. Acad. Sci. USA 43 509–512.
  • [9] Harris, T. E. (1959). On One-dimensional Neutron Multiplication. Research Memorandum RM-2317. RAND Corporation, Santa Monica, CA.
  • [10] Harris, T. and Bellman, R. (1952). On age-dependent binary branching processes. Ann. of Math. (2) 55 280–295.
  • [11] Jagers, P. (1975). Branching Processes with Biological Applications. Wiley, London.
  • [12] Jánossy, L. (1950). On the absorption of a nucleon cascade. Proc. Roy. Irish Acad. Sect. A. 53 181–188.
  • [13] Kesten, H. and Stigum, B. P. (1966). A limit theorem for multidimensional Galton–Watson processes. Ann. Math. Statist. 37 1211–1223.
  • [14] Kolmogorov, A. N. (1938). On the solution of a biological problem. Tomsk Univ. Proc 2 7–12.
  • [15] Mode, C. J. (1971). Multitype Branching Processes. Elsevier, New York.
  • [16] Ney, P. E. (1964). Generalized branching processes. I. Existence and uniqueness theorems. Illinois J. Math. 8 316–331.
  • [17] Ney, P. E. (1964). Generalized branching processes. II. Asymptotic theory. Illinois J. Math. 8 332–350.
  • [18] Sevastyanov, B. A. (1971). Branching Processes. Nauka, Moscow.
  • [19] Watson, H. W. and Galton, F. (1874). On the probability of extinction of families. J. Royal Anthropological Inst. 6 138–144.
  • [20] Yaglom, A. M. (1947). Certain limit theorems of the theory of branching random processes. Doklady Akad. Nauk SSSR (N.S.) 56 795–798.