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.
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