We consider the time evolution of the lattice subcritical Galton-Watson model with immigration. We prove Carleman type estimation for the cumulants in the simple case (binary splitting) and show the existence of a steady state. We also present the formula of the limiting distribution in a particular solvable case.

中文翻译：

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带移民的格子种群模型的稳态

我们考虑格子亚临界 Galton-Watson 模型随移民的时间演化。我们证明了简单情况（二元分裂）中累积量的卡尔曼类型估计，并证明了稳定状态的存在。我们还给出了特定可解情况下的极限分布公式。