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STS579 Anastasiia Rytova et al.
of a BRW with a finite variance tends to zero, but of a heavy-tailed BRW tends
to a positive constant. For ℤ , ≥ 3, the dimension of the lattice is already

large enough even for a BRW with a finite variance, in this case the underlying
random walk is transient, so that for both BRWs the population has a non-zero
probability of survival.

Acknowledgement
This work is supported by the Russian Foundation for Basic Research (grant
no. 17-01-0468).

References
1. Agbor, A., Molchanov, S., & Vainberg B. (2015). Global limit Theorems on
the convergence of multidimen-sional random walks to stable processes.
Stochastics and Dynamics.15(3): 1550024.
2. Albeverio, S., Bogachev, L. V., & Yarovaya E. B. (1998). Asymptotics of
branching symmetric random walk on the lattice with a single source.
C.R. Acad. Sci. Paris, Ser. I, Math.
3. Bolker, B. M., Pacala, S.W., & Neuhauser, C. (2003). Spatial dynamics in
model plant communities: what do we really know? Am. Nat. 162, 135–
148.
4. Borovkov, A., & Borovkov, K. (2008). Asymptotic Analysis of Random
Walks. Heavy-Tailed Distributions. Cambridge University Press.
5. Ermakova, E., Makhmutova, P., & Yarovaya, E. (2019). Branching random
walks and their applications for epidemic modeling. Stochastic Models,
DOI: 10.1080/15326349.2019.1572519
6. Feller, W. (1971). An introduction to probability theory and its
applications. Vol. II. Second edition. John Wiley & Sons, Inc., New York-
London-Sydney.
7. Haldane, J. B. S. (1927). A Mathematical Theory of Natural and Artificial
Selection, Part V: Selection and Mutation. PCPS 23(7): 838–844.
8. Khristolyubov, I., & Yarovaya, E. (2019). A Limit Theorem for Supercritical
Branching Random Walks with Branching Sources of Varying Intensity.
arXiv.org. URL: https://arxiv.org/pdf/1904.01468.
9. Molchanov, S., & Whitmeyer, J. (2017). Spatial Models of Population
Processes. In: Panov V. (eds) Mod¬ern Problems of Stochastic Analysis
and Statistics. MPSAS 2016. Springer Proceedings in Mathematics &
Statistics, vol 208. Springer, Cham.
10. Rytova, A. I., & Yarovaya, E. B. (2016). Multidimensional Watson lemma
and its applications. Mathemati-cal Notes, 99(3): 406–412.
11. Rytova, A., & Yarovaya, E. (2018). Survival Analysis of Particle Populations
in Branching Random Walks. arXiv.org. URL:
https://arxiv.org/abs/1812.09909.

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