带有移民的上临界Galton-Watson过程的Cramer中偏差

Cramer Moderate Deviations for a Supercritical Galton-Watson Process with Immigration

我们令{Xn;n≥0}是一个后代平均值为m的带有移民的上临界分支过程。Lotka-Nagaev估计量Xn1/Xn是用来估计后代均值的常用估计量。在本论文中,我们通过构造鞅得到了带有移民的Galton-Watson过程的Cramer中偏差结果。对于我们的证明,我们使用了著名的Cramer方法来证明自变量和的中偏差以满足我们的需要。

Let{Xn;n≥0}be a supercritical branching process with immigration and offspring mean m. The Lotka-Nagaev estimatorXn1/Xnis a common estimator for the offspring mean. In this paper, we establish some kinds of Cramer moderate deviation results for the Lotka-Nagaev estimator via a martingale method. For our proofs, we use the well-known Cramer method to prove the moderate deviation of the sum of independent variables to satisfy our needs.