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Branching Random Walks with Immigration

  • Dan Han
  • Yulia Makarova
  • Stanislav Molchanov
  • Elena Yarovaya
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10684)

Abstract

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.

Keywords

Branching random walks Multidimensional lattices Contact model Immigration Correlation functions 

Notes

Acknowledgments

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.

References

  1. Han, D., Molchanov, S., Whitmeyer, J.: Population processes with immigration. In: Panov, V. (ed.) Modern Problems of Stochastic Analysis and Statistics—Selected Contributions in Honor of Valentin Konakov, Springer, Heidelberg (2017), in pressGoogle Scholar
  2. Kolmogorov, A.N., Petrovskii, I.G., Piskunov, N.S.: A study of the diffusion equation with increase in the quality of matter, and its application to a biological problem. Bull. Moscow Univ. Math. Ser. A 1(6), 1–26 (1937). in RussianGoogle Scholar
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  4. Molchanov, S., Whitmeyer, J.: Spatial models of population processes. In: Panov, V. (ed.) Modern Problems of Stochastic Analysis and Statistics—Selected Contributions in Honor of Valentin Konakov, Springer, Heidelberg (2017), in pressGoogle Scholar
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  6. Yarovaya, E.B.: Branching random walks in a heterogeneous environment. Center of Applied Investigations of the Faculty of Mechanics and Mathematics of the Moscow State University, Moscow (2007), in RussianGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Dan Han
    • 1
  • Yulia Makarova
    • 2
  • Stanislav Molchanov
    • 1
    • 3
  • Elena Yarovaya
    • 2
  1. 1.University of North Carolina at CharlotteCharlotteUSA
  2. 2.Lomonosov Moscow State UniversityMoscowRussia
  3. 3.National Research University Higher School of EconomicsMoscowRussia

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