Geodesic
A limit theorem for supercritical random branching walks with branching sources of varying intensity
Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 3, pp. 456-480

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We consider a supercritical symmetric continuous-time branching random walk on a multidimensional lattice with a finite number of particle generation sources of varying positive intensities without any restrictions on the variance of jumps of the underlying random walk. It is assumed that the spectrum of the evolution operator contains at least one positive eigenvalue. We prove that under these conditions the largest eigenvalue of the evolution operator is simple and determines the rate of exponential growth of particle quantities at each point on the lattice as well as on the lattice as a whole.
Keywords: branching random walk, supercritical case, limit theorem, particle number exponential growth.
Mots-clés : multiple sources 
@article{TVP_2019_64_3_a2,
     author = {I. Khristolyubov and E. B. Yarovaya},
     title = {A limit theorem for supercritical random branching walks with branching sources of varying intensity},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {456--480},
     publisher = {mathdoc},
     volume = {64},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2019_64_3_a2/}
}
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I. Khristolyubov; E. B. Yarovaya. A limit theorem for supercritical random branching walks with branching sources of varying intensity. Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 3, pp. 456-480. http://geodesic.mathdoc.fr/item/TVP_2019_64_3_a2/