Branching Random Walks with Immigration
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 \(\mathbb Z^d\), \(d\ge 1\), 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.
KeywordsBranching random walks Multidimensional lattices Contact model Immigration Correlation functions
Yu. Makarova and E. Yarovaya were supported by the Russain Foundation for Basic Research (RFBR), project No. 17-01-00468. S. Molchanov was supported by the Russain Science Foundation (RSF), project No. 17-11-01098.
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