Filichkina, E.; Yarovaya, E. Branching Random Walks with One Particle Generation Center and Possible Absorption at Every Point. Mathematics2023, 11, 1676.
Filichkina, E.; Yarovaya, E. Branching Random Walks with One Particle Generation Center and Possible Absorption at Every Point. Mathematics 2023, 11, 1676.
Filichkina, E.; Yarovaya, E. Branching Random Walks with One Particle Generation Center and Possible Absorption at Every Point. Mathematics2023, 11, 1676.
Filichkina, E.; Yarovaya, E. Branching Random Walks with One Particle Generation Center and Possible Absorption at Every Point. Mathematics 2023, 11, 1676.
Abstract
We consider a new model of a branching random walk on a multidimensional lattice with continuous time and one source of particle reproduction and death, as well as an infinite number of sources in which, in addition to the walk, only absorption of particles can occur. The asymptotic behavior of the integer moments of both the total number of particles and the number of particles at a lattice point is studied depending on the relationship between the model parameters. In the case of the existence of an isolated positive eigenvalue of the evolution operator of the average number of particles, a limit theorem is obtained on the exponential growth of both the total number of particles and the number of particles at a lattice point.
Keywords
branching random walks; moments of particle numbers; evolution operator; Green’s function
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
