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Elementary new proofs of classical limit theorems for Galton–Watson processes

  • Jochen Geiger (a1)
Abstract

Classical results describe the asymptotic behaviour of a Galton–Watson branching process conditioned on non-extinction. We give new proofs of limit theorems in critical and subcritical cases. The proofs are based on the representation of conditioned Galton–Watson generation sizes as a sum of independent increments which is derived from the decomposition of the conditioned Galton–Watson family tree along the line of descent of the left-most particle.

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Postal address: Fachbereich Mathematik, Universität Frankfurt, Postfach 11 19 32, D-60054 Frankfurt am Main, Germany.
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Research supported by Deutsche Forschungsgemeinschaft.

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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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