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Steady states of lattice population models with immigration

Published on Aug 16, 2018in arXiv: Probability
Elena Chernousova2
Estimated H-index: 2
,
Yaqin Feng1
Estimated H-index: 1
+ 1 AuthorsJoseph M. Whitmeyer13
Estimated H-index: 13
Abstract
We consider the time evolution of the lattice subcritical Galton-Watson model with immigration. We prove Carleman type estimation for the cumulants in the simple case (binary splitting) and show the existence of a steady state. We also present the formula of the limiting distribution in a particular solvable case.
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The central result of this paper is the existence of limiting distributions for two classes of critical homogeneous-in-space branching processes with heavy tails spatial dynamics in dimension d = 2. In dimension d 鈮 3, the same results are true without any special assumptions on the underlying (non-degenerated) stochastic dynamics.
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