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Spread of a catalytic branching random walk on a multidimensional lattice

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  • Bulinskaya, Ekaterina Vl.

Abstract

For a supercritical catalytic branching random walk on Zd, d∈N, with an arbitrary finite catalysts set we study the spread of particles population as time grows to infinity. It is shown that in the result of the proper normalization of the particles positions in the limit there are a.s. no particles outside the closed convex surface in Rd which we call the propagation front and, under condition of infinite number of visits of the catalysts set, a.s. there exist particles on the propagation front. We also demonstrate that the propagation front is asymptotically densely populated and derive its alternative representation.

Suggested Citation

  • Bulinskaya, Ekaterina Vl., 2018. "Spread of a catalytic branching random walk on a multidimensional lattice," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2325-2340.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:7:p:2325-2340
    DOI: 10.1016/j.spa.2017.09.007
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    References listed on IDEAS

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    1. Bulinskaya, Ekaterina Vladimirovna, 2014. "Finiteness of hitting times under taboo," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 15-19.
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