On the convergence of the supercritical branching processes with immigration
Keyword(s):
It is shown for a supercritical branching process with immigration that if the log moment of the immigration distribution is infinite, then no sequence of positive constants {cn} exists such that {Xn/cn} converges in law to a proper limit distribution function F, except for the case F(0 +) = 1. Seneta's result [1] combined with the above-mentioned one imply that if 1 < m < ∞ then the finiteness of the log moment of the immigration distribution is a necessary and sufficient condition for the existence of some constants {cn} such that {Xn/cn} converges in law to a proper limit distribution function F, with F(0 +) < 1.
1977 ◽
Vol 14
(02)
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pp. 387-390
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1977 ◽
Vol 14
(04)
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pp. 702-716
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1975 ◽
Vol 12
(01)
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pp. 130-134
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1980 ◽
Vol 29
(3)
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pp. 337-347
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1988 ◽
Vol 28
(1)
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pp. 123-139
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