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

Author

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  • Elena Filichkina

    (Department of Probability Theory, Lomonosov Moscow State University, 119234 Moscow, Russia
    National Medical Research Center for Therapy and Preventive Medicine, 101990 Moscow, Russia
    These authors contributed equally to this work.)

  • Elena Yarovaya

    (Department of Probability Theory, Lomonosov Moscow State University, 119234 Moscow, Russia
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Elena Filichkina & Elena Yarovaya, 2023. "Branching Random Walks with One Particle Generation Center and Possible Absorption at Every Point," Mathematics, MDPI, vol. 11(7), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1676-:d:1112751
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    References listed on IDEAS

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    1. Elena B. Yarovaya, 2013. "Branching Random Walks With Several Sources-super-," Mathematical Population Studies, Taylor & Francis Journals, vol. 20(1), pages 14-26, March.
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    Cited by:

    1. Elena Filichkina & Elena Yarovaya, 2024. "Branching Random Walks on $$\mathbb {Z}$$ Z with One Particle Generation Center and Symmetrically Located Absorbing Sources," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-16, September.

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    2. Elena Filichkina & Elena Yarovaya, 2024. "Branching Random Walks on $$\mathbb {Z}$$ Z with One Particle Generation Center and Symmetrically Located Absorbing Sources," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-16, September.

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