A note on the L-convergence of a superadditive bisexual Galton-Watson process.
Miguel González, Manuel Molina (1998)
Extracta Mathematicae
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Miguel González, Manuel Molina (1998)
Extracta Mathematicae
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H. Hering (1977)
Annales de l'I.H.P. Probabilités et statistiques
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Klaus Fleischmann, Vitali Wachtel (2007)
Annales de l'I.H.P. Probabilités et statistiques
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K. Urbanik (1962)
Studia Mathematica
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Mitov, Kosto (1999)
Serdica Mathematical Journal
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This work is supported by Bulgarian NFSI, grant No. MM–704/97 The regenerative excursion process Z(t), t = 0, 1, 2, . . . is constructed by two independent sequences X = {Xi , i ≥ 1} and Z = {Ti , (Zi (t), 0 ≤ t < Ti ), i ≥ 1}. For the embedded alternating renewal process, with interarrival times Xi – the time for the installation and Ti – the time for the work, are proved some limit theorems for the spent worktime and the residual worktime, when at least one of the...
González, M., Molina, M. (1997)
Serdica Mathematical Journal
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A Superadditive Bisexual Galton-Watson Branching Process is considered and the total number of mating units, females and males, until the n-th generation, are studied. In particular some results about the stochastic monotony, probability generating functions and moments are obtained. Finally, the limit behaviour of those variables suitably normed is investigated.
S. C. Harris, R. Knobloch, A. E. Kyprianou (2010)
Annales de l'I.H.P. Probabilités et statistiques
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In the spirit of a classical result for Crump–Mode–Jagers processes, we prove a strong law of large numbers for fragmentation processes. Specifically, for self-similar fragmentation processes, including homogenous processes, we prove the almost sure convergence of an empirical measure associated with the stopping line corresponding to first fragments of size strictly smaller than for 1≥>0.