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.File in questo prodotto:
File | Dimensione | Formato | |
---|---|---|---|
1903.06157.pdf
accesso aperto
Descrizione: arXiv.org version
Tipologia:
Documento in Pre-print
Licenza:
Dominio pubblico
Dimensione
276.93 kB
Formato
Adobe PDF
|
276.93 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.