期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2003
卷号：65
期号：02
页码：229--248
出版社：Indian Statistical Institute
摘要：Let $(Z_t)_{0\le t<\infty}$ be a supercritical age-dependent branching process with offspring distribution $(p_j)_{j=0,1,2,\ldots}$, offspring mean $10$ is the Malthusian parameter defined by $m\int_0^\infty e^{-\al y} G(dy)=1$. In the case $\sum_{j=1}^\infty p_j \,j\log j<\infty$ Athreya (1969) has proven analytically that $\vp(s)$ is (up to a multiple constant) the unique solution of the above functional equation. In this paper we extend this result by a probabilistic argument assuming only that $1
