Branching Random Walks with Immigration. Lyapunov Stability


The paper contains several results on the existence of limits for the first two moments of the popular model in the population dynamics: continuous-time branching random walks on the multidimensional lattice Zd , d≥1 , with immigration and infinite number of initial particles. Additional result concerns the Lyapunov stability of the moments with respect to small perturbations of the parameters of the model such as mortality rate, the rate of the birth of (n−1) offsprings and, finally, the immigration rate.

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