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Steady state for the subcritical contact branching random walk on the lattice with the arbitrary number of offspring and 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 subcritical contact branching random walk on Zd in continuous time with the arbitrary number of offspring and with immigration. We prove the existence of the steady state (statistical equilibrium).
  • References (6)
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References6
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#1Dan Han (UNCC: University of North Carolina at Charlotte)H-Index: 1
#2Stanislav Molchanov (UNCC: University of North Carolina at Charlotte)H-Index: 28
Last. Joseph M. Whitmeyer (UNCC: University of North Carolina at Charlotte)H-Index: 13
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The paper contains a complete analysis of the Galton鈥揥atson models with immigration, including the processes in the random environment, stationary or nonstationary ones. We also study the branching random walk on \(Z^{d}\) with immigration and prove the existence of the limits for the first two correlation functions.
3 CitationsSource
#1S. A. Molchanov (UNCC: University of North Carolina at Charlotte)H-Index: 1
#2E. B. Yarovaya (MSU: Moscow State University)H-Index: 1
An important role in the theory of branching random walks is played by the problem of the spectrum of a bounded symmetric operator, the generator of a random walk on a multidimensional integer lattice, with a one-point potential. We consider operators with potentials of a more general form that take nonzero values on a finite set of points of the integer lattice. The resolvent analysis of such operators has allowed us to study branching random walks with large deviations. We prove limit theorems...
4 CitationsSource
#1Yuri Kondratiev (Bielefeld University)H-Index: 25
#2Oleksandr Kutoviy (Bielefeld University)H-Index: 13
Last. Sergey Pirogov (RAS: Russian Academy of Sciences)H-Index: 6
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We study the continuous version of the contact model. Using an analytic approach, we construct the non-equilibrium contact process as a Markov process on configuration space. The construction is based on the analysis of correlation functions evolution. The problem concerning invariant measures as well as asymptotics of correlation functions are also studied.
58 CitationsSource
#1William FellerH-Index: 46
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#1A. N. KolmogorovH-Index: 1
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