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Moscow Mathematical Journal, 2019, Volume 19, Number 1, Pages 7–36
DOI: https://doi.org/10.17323/1609-4514-2019-19-1-7-36
(Mi mmj698)
 

This article is cited in 5 scientific papers (total in 5 papers)

Lattice birth-and-death processes

Viktor Bezborodov, Yuri Kondratiev, Oleksandr Kutoviy

Fakultät für Mathematik, Universität Bielefeld, Universitätsstr. 25, 33615 Bielefeld, Germany
Full-text PDF Citations (5)
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Abstract: Lattice birth-and-death Markov dynamics of particle systems with spins from $\mathbb{Z} _+$ 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.
Key words and phrases: birth-death process, interacting particle systems, stochastic equation with Poisson noise, martingale problem, invariant measure, Bolker–Pacala model.
Bibliographic databases:
Document Type: Article
MSC: 60K35, 82C22
Language: Russian
Citation: Viktor Bezborodov, Yuri Kondratiev, Oleksandr Kutoviy, “Lattice birth-and-death processes”, Mosc. Math. J., 19:1 (2019), 7–36
Citation in format AMSBIB
\Bibitem{BezKonKut19}
\by Viktor~Bezborodov, Yuri~Kondratiev, Oleksandr~Kutoviy
\paper Lattice birth-and-death processes
\jour Mosc. Math.~J.
\yr 2019
\vol 19
\issue 1
\pages 7--36
\mathnet{http://mi.mathnet.ru/mmj698}
\crossref{https://doi.org/10.17323/1609-4514-2019-19-1-7-36}
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  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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