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Branching Particle Systems and Dawson-Watanabe Superprocesses

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Part of the Lecture Notes in Mathematics book series (LNMECOLE,volume 1781)

Abstract

Let \( \{ X_i^k :i \in \mathbb{N},k \in \mathbb{Z}_ + \} \) be i.i.d. \( \mathbb{Z}_ + \)-valued random variables with mean 1 and variance γ > 0. We think of \( X_i^k \) as the number of offspring of the {iti}{suth} individual in the {itk}{suth} generation, so that \( Z_{k + 1} = \sum\limits_{i = 1}^{z_k } {X_i^k (set Z_0 \equiv 1)} \) is the size of the {itk} + 1{sust} generation of a Galton-Watson branching process with offspring distribution ℒ \( (X_i^k ) \), the law of \( X_i^k \).

Keywords

  • Polish Space
  • Martingale Problem
  • Strong Markov Property
  • Canonical Measure
  • Weak Limit Point

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© 2002 Springer-Verlag Berlin Heidelberg

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(2002). Branching Particle Systems and Dawson-Watanabe Superprocesses. In: Bernard, P. (eds) Lectures on Probability Theory and Statistics. Lecture Notes in Mathematics, vol 1781. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47944-9_6

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  • DOI: https://doi.org/10.1007/3-540-47944-9_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43736-9

  • Online ISBN: 978-3-540-47944-4

  • eBook Packages: Springer Book Archive