Abstract
Consideration is given to the continuous-time supercritical branching random walk over a multidimensional lattice with a finite number of particle generation sources of the same intensity both with and without constraint on the variance of jumps of random walk underlying the process. Asymptotic behavior of the Green function and eigenvalue of the evolution operator of the mean number of particles under source intensity close to the critical one was established.
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Acknowledgements
This study has been carried out at Steklov Mathematical Institute of Russian Academy of Sciences, and was supported by the Russian Science Foundation, project no. 14-21-00162.
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Yarovaya, E. Operator Equations of Branching Random Walks. Methodol Comput Appl Probab 21, 1007–1021 (2019). https://doi.org/10.1007/s11009-017-9590-3
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DOI: https://doi.org/10.1007/s11009-017-9590-3
Keywords
- Branching random walks
- Green function
- Convolution-type operator
- Multipoint perturbations
- Positive eigenvalues