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Statistica Sinica 20 (2010), 1273-1289





A FLUCTUATION LIMIT THEOREM OF BRANCHING

PROCESSES AND ITS APPLICATIONS


Shan Yang


Iowa State University


Abstract: We prove that the fluctuation limit of a sequence of Galton-Watson branching processes with immigration can be an Ornstein-Uhlenbeck type process under some assumptions on the offspring and the immigration laws. The asymptotic properties of the conditional least square estimators of the offspring mean and the immigration mean are studied when the limit process is an Ornstein-Uhlenbeck diffusion process.



Key words and phrases: Conditional least square estimator, fluctuation limit, Galton-Watson branching process with immigration, Lévy process, Ornstein-Uhlenbeck type process.

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