Asymptotic Behaviors for Critical Branching Processes with Immigration |
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Authors: | Li Dou Dou Zhang Mei |
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Institution: | School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing 100875, P. R. China |
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Abstract: | In this paper, we investigate the asymptotic behaviors of the critical branching process with immigration {Zn, n ≥ 0}. First we get some estimation for the probability generating function of Zn. Based on it, we get a large deviation for Zn+1/Zn. Lower and upper deviations for Zn are also studied. As a by-product, an upper deviation for max1≤i≤n Zi is obtained. |
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Keywords: | Critical branching process immigration large deviations |
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