论文标题
关于具有依赖移民的分支过程的功能极限定理
On functional limit theorems for branching processes with dependent immigration
论文作者
论文摘要
在本文中，我们考虑了具有非平稳移民的三角分支过程。我们证明，正确归一化的分支过程的趋势趋于地融合了移民，以确定性功能，假设移民为行$ψ-$混合，而后代平均值倾向于其临界值1，移民平均值和通过常规变化功能控制的移民均值和方差。此外，当移民为$ m-m $依赖时，我们获得了分支过程的波动定理，而$ m $可能会以一定的速度与行指数无限。在这种情况下，限制过程是一个时间变化的维纳过程。我们的结果扩展并改善了文献中先前的已知结果。
In this paper we consider a triangular array of branching processes with non-stationary immigration. We prove a weak convergence of properly normalized branching processes with immigration to deterministic function under assumption that immigration is rowwise $ψ-$mixing and the offspring mean tends to its critical value 1, immigration mean and variance controlled by regularly varying functions. Moreover, we obtain a fluctuation limit theorem for branching process with immigration when immigration is $m-$dependent where $m$ may tend to infinity with the row index at a certain rate. In this case the limiting process is a time-changed Wiener process. Our results extend and improve the previous known results in the literature.
