Advances in continuous and discrete models最新文献

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Some properties of branching processes with random control functions and affected by viral infectivity in random environments. 随机环境中受病毒感染性影响的具有随机控制函数的分支过程的一些性质。

Advances in continuous and discrete models

Pub Date : 2023-01-01 DOI: 10.1186/s13662-023-03775-3

Min Ren, Guanghui Zhang

In this paper, a model of branching processes with random control functions and affected by viral infectivity in independent and identically distributed random environments is established, and the Markov property of the model and a sufficient condition for the model to be certainly extinct under some conditions are discussed. Then, the limit properties of the model are studied. Under the normalization factor ${S_{n} : n \in N}$ , the normalization processes ${{\hat{W}}_{n} : n \in N}$ are studied, and the sufficient conditions of ${{\hat{W}}_{n} : n \in N}$ a.s., $L^{1}$ and $L^{2}$ convergence are given; A sufficient condition and a necessary condition for convergence to a nondegenerate at zero random variable are obtained. Under the normalization factor ${I_{n} : n \in N}$ , the normalization processes ${{\bar{W}}_{n} : n \in N}$ are studied, and the sufficient conditions of ${{\bar{W}}_{n} : n \in N}$ a.s., and $L^{1}$ convergence are obtained.

本文建立了独立同分布随机环境中受病毒感染的具有随机控制函数的分支过程模型，讨论了该模型的马尔可夫性质和在某些条件下该模型肯定绝灭的充分条件。然后，研究了模型的极限性质。在归一化因子{Sn:n∈n}下，研究了归一化过程{W′n:n∈n}，并给出了{W′n:n∈n} as、L1、L2收敛的充分条件;得到了在零随机变量处收敛到非退化的充分条件和必要条件。在归一化因子{In:n∈n}下，研究了归一化过程{W¯n:n∈n}，得到了{W¯n:n∈n} a.s.和L1收敛的充分条件。

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