In this article, the population-size-dependent bisexual Galton-Watson processes are considered. Under some suitable conditions on the mating functions and the offspring distribution, existence of the limit of mean gro...In this article, the population-size-dependent bisexual Galton-Watson processes are considered. Under some suitable conditions on the mating functions and the offspring distribution, existence of the limit of mean growth rate per mating unit is proved. And based on the limit, a criterion to identify whether the process admits ultimate extinct with probability one is obtained.展开更多
The class of population-size-dependent branching processes in independent identically distributed random environments is investigated. Under the critical case and appropriate moment assumption, we establish an asympto...The class of population-size-dependent branching processes in independent identically distributed random environments is investigated. Under the critical case and appropriate moment assumption, we establish an asymptotic estimate of the survival probability at generation n.展开更多
文摘In this article, the population-size-dependent bisexual Galton-Watson processes are considered. Under some suitable conditions on the mating functions and the offspring distribution, existence of the limit of mean growth rate per mating unit is proved. And based on the limit, a criterion to identify whether the process admits ultimate extinct with probability one is obtained.
基金Supported by the National Natural Science Foundation of China(No.11301133 and 11471218)the Natural Science Foundation of Hebei province(No.A2014202236 and A2014202052)
文摘The class of population-size-dependent branching processes in independent identically distributed random environments is investigated. Under the critical case and appropriate moment assumption, we establish an asymptotic estimate of the survival probability at generation n.
