Asymptotic behavior of critical irreducible multi-type continuous state and continuous time branching processes with immigration
Asymptotic behavior of critical irreducible multi-type continuous state and continuous time branching processes with immigration
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DOI：
10.1142/s0219493716500088
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发表时间：
2014-04
期刊：
影响因子：
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通讯作者：
M. Barczy;G. Pap
中科院分区：
文献类型：
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作者：
M. Barczy;G. Pap
在自然假设下，对具有移民的临界、不可约多型连续状态和连续时间分支过程，给出了一个Feller型扩散逼近。也就是说，它被证明了一个适当的规模的随机阶跃函数序列形成的临界，不可约的多型连续状态和连续时间的分支过程与移民弱收敛到平方贝塞尔过程所支持的射线所确定的矩阵的Perron向量有关的分支过程的分支机制的问题。
Under natural assumptions, a Feller type diffusion approximation is derived for critical, irreducible multi-type continuous state and continuous time branching processes with immigration. Namely, it is proved that a sequence of appropriately scaled random step functions formed from a critical, irreducible multi-type continuous state and continuous time branching process with immigration converges weakly towards a squared Bessel process supported by a ray determined by the Perron vector of a matrix related to the branching mechanism of the branching process in question.