AI 中文总结
研究具有相关迁入的临界分支过程序列的扩散近似，在一般假设下，证明其缩放和归一化序列依分布收敛到扩散过程，扩展了魏和温尼基（1989）的泛函极限定理。
AI 中文摘要
本文旨在研究具有严格平稳和遍历迁入的临界分支过程序列的扩散近似。在对迁入序列的依赖结构有相当一般的假设下，我们证明了具有迁入的分支过程的缩放和适当归一化序列在斯科罗霍德拓扑中依分布收敛到扩散过程。我们的结果将魏和温尼基（1989）的泛函极限定理扩展到了迁入序列相关的情况。
英文摘要
This paper aims to investigate a diffusion approximation of a sequence of critical branching processes with strictly stationary and ergodic immigration. Under fairly general assumptions on the dependence structure of the immigration sequence, we establish that the scaled and properly normalized sequence of branching processes with immigration converges in distribution to the diffusion process in the Skorokhod topology. Our result extends the functional limit theorem of Wei and Winnicki (1989) to the case where the immigration sequence is dependent.
Comments19 pages
