Fecundity regulation in a spatial birth-and-death process

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.

Type
Publication
Stochastics and Dynamics