带拯救的广义非线性Markov分枝模型的稳定性

Abstract

Abstract:

In this paper, the generalized non-linear Markov branching model with resurrection is considered. Some properties of the generating functions for generalized non-linear Markov branching q-matrix with resurrection are firstly investigated. By using the generating functions of the corresponding q-matrix, the criteria for regularity and uniqueness for such structure are firstly established, and the explicit expressions for the extinction probabilities and mean extinction times are presented. The stability properties and ergodicity of the model with resurrection are then investigated. The conditions for recurrence, ergodicity are obtained. An explicit expression for the equilibrium distribution is further presented.

Key words: Generalized non-linear Markov branching process, Resurrection, Regularity, Ergodicity

CLC Number:

O211.6

Zhang Lina, Li Junping, Geng Shifeng. The Stability Property of Generalized Nonlinear Markov Branching Models with Resurrection[J].Acta mathematica scientia,Series A, 2015, 35(6): 1190-1206.

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References

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The Stability Property of Generalized Nonlinear Markov Branching Models with Resurrection

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