Geodesic
Periodic branching random walk on $\mathbf {Z}^d$ with immigration
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 35, Tome 526 (2023), pp. 90-108

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We consider a continuous-time branching random walk with immigration on $\mathbf {Z}^d$ with branching sources located periodically. The asymptotic behavior of the mean number of particles at an arbitrary point is obtained for $t\to\infty$ in the supercritical and subcritical cases. 
@article{ZNSL_2023_526_a5,
     author = {I. I. Lukashova},
     title = {Periodic branching random walk on $\mathbf {Z}^d$ with immigration},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {90--108},
     publisher = {mathdoc},
     volume = {526},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_526_a5/}
}
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I. I. Lukashova. Periodic branching random walk on $\mathbf {Z}^d$ with immigration. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 35, Tome 526 (2023), pp. 90-108. http://geodesic.mathdoc.fr/item/ZNSL_2023_526_a5/