arXiv:1903.06157 [math.PR]AbstractReferencesReviewsResources
Fecundity regulation in a spatial birth-and-death process
Viktor Bezborodov, Luca Di Persio, Dmitri Finkelshtein, Yuri Kondratiev, Oleksandr Kutoviy
Published 2019-03-14Version 1
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 find also sufficient conditions that the degenerate invariant distribution is unique for the considered process.
Categories: math.PR
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