We study a Markov birth-and-death process on a space of locally finite configurations, which describes an ecological model with a density-dependent fecundity regulation mechanism. We establish existence and uniqueness of this process and analyze its properties. In particular, we show global time-space boundedness of the population density and, using a constructed Foster–Lyapunov-type function, we study return times to certain level sets of tempered configurations. We also find sufficient conditions that the degenerate invariant distribution is unique for the considered process.

Fecundity regulation in a spatial birth-and-death process

Bezborodov, Viktor;Di Persio, Luca
;
2021-01-01

Abstract

We study a Markov birth-and-death process on a space of locally finite configurations, which describes an ecological model with a density-dependent fecundity regulation mechanism. We establish existence and uniqueness of this process and analyze its properties. In particular, we show global time-space boundedness of the population density and, using a constructed Foster–Lyapunov-type function, we study return times to certain level sets of tempered configurations. We also find sufficient conditions that the degenerate invariant distribution is unique for the considered process.
2021
Measure-valued process , Markov evolution , individual-based models , spatial birth-and-death dynamics , spatial ecology , density-dependent fecundity
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/1018241
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