Fluctuation limit of branching processes with immigration and estimation of the means
2005 ◽
Vol 37
(02)
◽
pp. 523-538
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Keyword(s):
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.
2005 ◽
Vol 37
(2)
◽
pp. 523-538
◽
2003 ◽
Vol 40
(3)
◽
pp. 750-765
◽
2005 ◽
Vol 93
(2)
◽
pp. 375-393
◽
2007 ◽
Vol 39
(4)
◽
pp. 1054-1069
◽
2003 ◽
Vol 40
(03)
◽
pp. 750-765
◽
2007 ◽
Vol 39
(04)
◽
pp. 1054-1069
◽
Keyword(s):