Lattice birth-and-death processes

Viktor Bezborodov; Yuri Kondratiev; Oleksandr Kutoviy

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arXiv · 1506.04309

Lattice birth-and-death processes

Viktor Bezborodov·Yuri Kondratiev·Oleksandr Kutoviy

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Abstract

Lattice birth-and-death Markov dynamics of particle systems with spins from the set of non-negative integers are constructed as unique solutions to certain stochastic equations. Pathwise uniqueness, strong existence, Markov property and joint uniqueness in law are proven, and a martingale characterization of the process is given. Sufficient conditions for the existence of an invariant distribution are formulated in terms of Lyapunov functions. We apply obtained results to discrete analogs of the Bolker--Pacala--Dieckmann--Law model and an aggregation model.

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Viktor Bezborodov, Yuri Kondratiev, Oleksandr Kutoviy. 2015-06-13. Lattice birth-and-death processes. https://arxiv.org/abs/1506.04309

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