Lattice Birth-And-Death Processes

Bezborodov V, Kondratiev Y, Kutovyi O (2019)
Moscow Mathematical Journal 19(1): 7-36.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
Lattice birth-and-death Markov dynamics of particle systems with spins from 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.
Stichworte
Birth-death process; interacting particle systems; stochastic equation; with Poisson noise; martingale problem; invariant measure; Bolker-Pacala; model
Erscheinungsjahr
2019
Zeitschriftentitel
Moscow Mathematical Journal
Band
19
Ausgabe
1
Seite(n)
7-36
ISSN
1609-3321
eISSN
1609-4514
Page URI
https://pub.uni-bielefeld.de/record/2936967

Zitieren

Bezborodov V, Kondratiev Y, Kutovyi O. Lattice Birth-And-Death Processes. Moscow Mathematical Journal . 2019;19(1):7-36.
Bezborodov, V., Kondratiev, Y., & Kutovyi, O. (2019). Lattice Birth-And-Death Processes. Moscow Mathematical Journal , 19(1), 7-36. doi:10.17323/1609-4514-2019-19-1-7-36
Bezborodov, V., Kondratiev, Y., and Kutovyi, O. (2019). Lattice Birth-And-Death Processes. Moscow Mathematical Journal 19, 7-36.
Bezborodov, V., Kondratiev, Y., & Kutovyi, O., 2019. Lattice Birth-And-Death Processes. Moscow Mathematical Journal , 19(1), p 7-36.
V. Bezborodov, Y. Kondratiev, and O. Kutovyi, “Lattice Birth-And-Death Processes”, Moscow Mathematical Journal , vol. 19, 2019, pp. 7-36.
Bezborodov, V., Kondratiev, Y., Kutovyi, O.: Lattice Birth-And-Death Processes. Moscow Mathematical Journal . 19, 7-36 (2019).
Bezborodov, Viktor, Kondratiev, Yuri, and Kutovyi, Oleksandr. “Lattice Birth-And-Death Processes”. Moscow Mathematical Journal 19.1 (2019): 7-36.