摘要
In this paper,a critical Galton-Watson branching process {Z_(n)} is considered.Large deviation rates of SZ_(n):=Σ_(i=1)^_(Z_(n)) Xi are obtained,where {X_(i);i≥1} is a sequence of independent and identically distributed random variables and X_(1) is in the domain of attraction of an-stable law with α∈(0,2).One shall see that the convergence rate is determined by the tail index of X_(1) and the variance of Z_(1).Our results can be compared with those ones of the supercritical case.
基金
supported by the National Natural Science Foundation of China(No.12101023,No.11871103 and 12271043)
the National Key Research and Development Program of China(No.2020YFA0712900)
Fundamental Research Funds for the Central Universities(No.2023MS077).
