Fecundity regulation in a spatial birth-and-death process

2019/03/14 by Bezborodov, Viktor, Di Persio, Luca, Finkelshtein, Dmitri +2 · 1 citation
#60G55 #60J25 #82C21 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1903.06157

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 find also sufficient conditions that the degenerate invariant distribution is unique for the considered process.

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• Stochastic dynamics on evolving geometric graphs

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