Geodesic
Clustering effect for multitype branching random walk
Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 3, pp. 443-455 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a time-continuous symmetric branching random walk over a multidimensional lattice with particles of several types and a Markov branching process at each point of the lattice. It is assumed that initially at each lattice point there is one particle of each type, and any particle can produce an arbitrary number of descendants of each type in the process of branching. For the transient random walk and the critical branching process, the effect of spatial clusterization of the population particles is studied.
Keywords: branching random walk, critical branching process, clustering effect. 
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     author = {D. M. Balashova},
     title = {Clustering effect for multitype branching random walk},
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D. M. Balashova. Clustering effect for multitype branching random walk. Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 3, pp. 443-455. http://geodesic.mathdoc.fr/item/TVP_2022_67_3_a1/

[1] D. Balashova, S. Molchanov, E. Yarovaya, “Structure of the particle population for a branching random walk with a critical reproduction law”, Methodol. Comput. Appl. Probab., 23:1 (2021), 85–102 | DOI | MR | Zbl

[2] I. Makarova, D. Balashova, S. Molchanov, E. Yarovaya, “Branching random walks with two types of particles on multidimensional lattices”, Mathematics, 10:6 (2022), 867, 45 pp. | DOI

[3] S. A. Molchanov, E. B. Yarovaya, “Large deviations for a symmetric branching random walk on a multidimensional lattice”, Proc. Steklov Inst. Math., 282 (2013), 186–201 | DOI | MR | Zbl

[4] D. M. Balashova, E. B. Yarovaya, “Structure of the population of particles for a branching random walk in a homogeneous environment”, Proc. Steklov Inst. Math., 316 (2022), 57–71 | DOI | DOI | Zbl

[5] I. I. Gihman, A. V. Skorohod, The theory of stochastic processes, v. II, Grundlehren Math. Wiss., 218, Springer-Verlag, New York–Heidelberg, 1975, vii+441 pp. | MR | MR | Zbl | Zbl

[6] B. A. Sewastjanow, Verzweigungsprozesse, Math. Lehrbücher Monogr. II. Abt. Math. Monogr., 34, Akademie-Verlag, Berlin, 1974, xi+326 pp. | MR | MR | Zbl | Zbl

[7] E. B. Yarovaya, Vetvyaschiesya sluchainye bluzhdaniya v neodnorodnoi srede, Tsentr prikl. issled. pri mekh.-matem. f-te MGU, M., 2007, 104 pp.