We prove that a spatial birth-and-death process is both ϕϕ-irreducible and ψψ-irreducible under rather general conditions on the birth and death rates. It is also shown that every maximal irreducibility measure is equivalent to the Lebesgue-Poisson measure on the space of finite configuration.

Maximal irreducibility measure for spatial birth-and-death processes

DI PERSIO, Luca
;
BEZBORODOV, VIKTOR
2017-01-01

Abstract

We prove that a spatial birth-and-death process is both ϕϕ-irreducible and ψψ-irreducible under rather general conditions on the birth and death rates. It is also shown that every maximal irreducibility measure is equivalent to the Lebesgue-Poisson measure on the space of finite configuration.
Birth-and-death processes; Maximal irreducibility measure; Markov chain; Lebesgue-Poisson measure; ϕ-irreducibility
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/959051
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