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Branching Random Walks with Immigration

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Analytical and Computational Methods in Probability Theory (ACMPT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10684))

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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.

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References

  • 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 press

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  • 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 press

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  • Oksendal, B.: Stochastic Differential Equations. An Inroduction with Applications., 6th edn. Springer, Heidelberg (2005)

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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.

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Authors and Affiliations

  1. University of North Carolina at Charlotte, Charlotte, NC, 28223, USA

    Dan Han & Stanislav Molchanov

  2. Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119234, Russia

    Yulia Makarova & Elena Yarovaya

  3. National Research University Higher School of Economics, Mysnitskaya str., Moscow, 101000, Russia

    Stanislav Molchanov

Authors
  1. Dan Han
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  2. Yulia Makarova
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  3. Stanislav Molchanov
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  4. Elena Yarovaya
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Corresponding author

Correspondence to Elena Yarovaya .

Editor information

Editors and Affiliations

  1. Department of Applied Probability and Informatics, RUDN University, Moscow, Russia

    Vladimir V. Rykov

  2. City University of Hong Kong, Hong Kong, Hong Kong

    Nozer D. Singpurwalla

  3. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

    Andrey M. Zubkov

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Han, D., Makarova, Y., Molchanov, S., Yarovaya, E. (2017). Branching Random Walks with Immigration. In: Rykov, V., Singpurwalla, N., Zubkov, A. (eds) Analytical and Computational Methods in Probability Theory. ACMPT 2017. Lecture Notes in Computer Science(), vol 10684. Springer, Cham. https://doi.org/10.1007/978-3-319-71504-9_33

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  • DOI: https://doi.org/10.1007/978-3-319-71504-9_33

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71503-2

  • Online ISBN: 978-3-319-71504-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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