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On the geometric growth in controlled branching processes with random control function

  • M. González (a1), M. Molina (a1) and I. del Puerto (a1)


The limit behaviour of a controlled branching process with random control function is investigated. A necessary condition and a sufficient condition for the geometric growth of such a process are established by considering the L 1-convergence. Finally, taking into account the classical X log+ X criterion in branching processes, a necessary and sufficient condition is provided.


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Postal address: Departamento de Matemáticas, Facultad de Ciencias, 06071 Badajoz, Spain
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Bruss, F. T. (1980). A counterpart of the Borel—Cantelli lemma. J. Appl. Prob. 17, 10941101.
Dion, J. P., and Essebbar, B. (1995). On the Statistics of Controlled Branching Processes (Lecture Notes Statist. 99). Springer, New York, pp. 1421.
Feller, W. (1968). An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd edn. John Wiley, New York.
González, M., Molina, M., and del Puerto, I. (2002). On the class of controlled branching process with random control functions. J. Appl. Prob. 39, 804815.
Klebaner, F. (1984). Geometric rate of growth in population-size-dependent branching processes. J. Appl. Prob. 21, 4049.
Klebaner, F. (1985). A limit theorem for population-size-dependent branching processes. J. Appl. Prob. 22, 4857.
Nakagawa, T. (1994). The Lα (1<α≤ 2) convergence of a controlled branching process in a random environment. Bull. Gen. Ed. Dokkyo Univ. School Medicine 17, 1724.
Sevastýanov, B. A., and Zubkov, A. M. (1974). Controlled branching processes. Theory Prob. Appl. 19, 1424.
Yanev, N. M. (1976). Conditions for degeneracy of ϕ-branching processes with random ϕ. Theory Prob. Appl. 20, 421428.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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