Fluctuation limit of branching processes with immigration and estimation of the means
Fluctuation limit of branching processes with immigration and estimation of the means
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DOI：
10.1239/aap/1118858637
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发表时间：
2005-06
影响因子：
1.2
通讯作者：
M. Ispány;G. Pap;M. V. van Zuijlen
中科院分区：
文献类型：
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作者：
M. Ispány;G. Pap;M. V. van Zuijlen
研究了一类带移民的Galton-Watson分枝过程序列，其中后代均值趋于临界值1，后代方差趋于0。结果表明，波动极限是一个Ornstein-Uhlenbeck型过程。因此，在相反的情况下，其中的后代方差趋于一个积极的限制，它的后代均值的条件最小二乘估计是渐近正态的。规范因子是n 3/2，与次临界情况（其中规范因子是n 1/2）和具有正的极限子代方差的近临界情况（其中规范因子是n）形成对比。
We investigate a sequence of Galton-Watson branching processes with immigration, where the offspring mean tends to its critical value 1 and the offspring variance tends to 0. It is shown that the fluctuation limit is an Ornstein-Uhlenbeck-type process. As a consequence, in contrast to the case in which the offspring variance tends to a positive limit, it transpires that the conditional least-squares estimator of the offspring mean is asymptotically normal. The norming factor is n 3/2, in contrast to both the subcritical case, in which it is n 1/2, and the nearly critical case with positive limiting offspring variance, in which it is n.