标题： 具有 Immigration 的临界原始多类型分支过程的渐近行为 显示英文标题

标题： Asymptotic behavior of critical primitive multi-type branching processes with immigration

摘要： 在自然假设下，当子代均值矩阵是本原的（换句话说，正则的）情况下，得到了临界多类型分支过程带移民的Feller型扩散逼近。具体来说，证明了由一列临界本原多类型分支过程带移民形成的适当缩放的随机步函数序列在弱收敛意义下趋近于一个平方Bessel过程，该过程支持由子代均值矩阵的Perron向量确定的射线。 显示英文摘要

摘要： Under natural assumptions a Feller type diffusion approximation is derived for critical multi-type branching processes with immigration when the offspring mean matrix is primitive (in other words, positively regular). Namely, it is proved that a sequence of appropriately scaled random step functions formed from a sequence of critical primitive multi-type branching processes with immigration converges weakly towards a squared Bessel process supported by a ray determined by the Perron vector of the offspring mean matrix.