Branching Random Walks with One Particle Generation Center and Possible Absorption at Every Point

Elena Filichkina and Elena Yarovaya ()
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Elena Filichkina: Department of Probability Theory, Lomonosov Moscow State University, 119234 Moscow, Russia
Elena Yarovaya: Department of Probability Theory, Lomonosov Moscow State University, 119234 Moscow, Russia

Mathematics, 2023, vol. 11, issue 7, 1-16

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 the 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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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