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Some properties of branching processes with random control functions and affected by viral infectivity in random
1Suzhou, 234000 China College of Mathematics and Statistics, Suzhou University.
Abstract:
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 , the normalization processes are studied, and the sufficient conditions of a.s., and 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 , the normalization processes are studied, and the sufficient conditions of a.s., and convergence are obtained.
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