Local limit theorems for the critical galton-watson process with immigration
Authors
Mellein, Bernhard
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Content type
Artículo de revista
Document language
EspañolPublication date
1982
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Abstract
Este artículo considera un proceso de ramificación critico de Galton-Watson con inmigración, en el cual la distribución aperiódica de nacimientos {P0,P1,...} satisface una condición de tipo j2 log j, [Formula Matemática] la distribución de inmigración satisface una condición de tipo j log j. Se establece el comportamiento asintótico de las probabilidades de transición en el paso n cuando n → ∞, j → i/n, j/n permanecen acotadas. Como aplicación, se obtiene el comportamiento asintótico de la medida invariante del proceso.
This paper considers a critical Galton-Watson branching process with immigration, in which the aperiodic offspring distribution {P0,P1,...} satisfies a j2 log j-condition [Formula Matemática] and the immigration distribution a j log j-condition. The asymptotic behavior of the n-step transition probabilities Pn(i,j) ad n + ∞, and i/n and j/n remain bounded, is established. As an application of this result the asymptotic behavior of the invariant measure of the process is obtained.
This paper considers a critical Galton-Watson branching process with immigration, in which the aperiodic offspring distribution {P0,P1,...} satisfies a j2 log j-condition [Formula Matemática] and the immigration distribution a j log j-condition. The asymptotic behavior of the n-step transition probabilities Pn(i,j) ad n + ∞, and i/n and j/n remain bounded, is established. As an application of this result the asymptotic behavior of the invariant measure of the process is obtained.