随机指标分枝过程的渐进性质

Asymptotic properties of a Poisson randomly indexed branching process

考虑一个Galton-Watson过程{Zt}和一个独立的Poisson过程{Nt},证明了连续时间过程{ZNt}是一个齐次连续时间马氏链.记f(t;s)为{ZNt}的生成函数,我们研究了f(t;s)的一些经典渐进性质.这些结果将应用于统计推断,生存概率和{ZNt}的条件极限定理.

Consider a Galton-Watson process Z n and an independent Poisson process N t,the continuous time process Z N t is a Poisson randomly indexed branching process.We show that Z N t is a homogenous continuous time Markov chain.Let f(t;s)be the generating function of Z N t.We obtain some classical asymptotic properties of f(t;s).These results are applied to the statistical inference,the survival probability and the conditional limit theorem of Z N t.