Geodesic
On the sojourn time distribution of a~random walk at a~multidimensional lattice point
Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 4, pp. 657-675

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We consider critical symmetric branching random walks on a multidimensional lattice with continuous time and with the source of particle birth and death at the origin. We prove limit theorems on the distribution of the sojourn time of the underlying random walk at a point depending on the lattice dimension under the assumption of finite variance and under a condition leading to infinite variance of jumps. We study the limit distribution of the population of particles at the source for recurrent critical branching random walks.
Keywords: branching random walk, multidimensional lattice, particle population distribution at a lattice point, variance of jumps, functional limit theorem, method of moments. 
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     author = {A. A. Aparin and G. A. Popov and E. B. Yarovaya},
     title = {On the sojourn time distribution of a~random walk at a~multidimensional lattice point},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {657--675},
     publisher = {mathdoc},
     volume = {66},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2021_66_4_a2/}
}
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A. A. Aparin; G. A. Popov; E. B. Yarovaya. On the sojourn time distribution of a~random walk at a~multidimensional lattice point. Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 4, pp. 657-675. http://geodesic.mathdoc.fr/item/TVP_2021_66_4_a2/