Fecundity regulation in a spatial birth-and-death process
Probability
2019-03-15 v1
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.
Cite
@article{arxiv.1903.06157,
title = {Fecundity regulation in a spatial birth-and-death process},
author = {Viktor Bezborodov and Luca Di Persio and Dmitri Finkelshtein and Yuri Kondratiev and Oleksandr Kutoviy},
journal= {arXiv preprint arXiv:1903.06157},
year = {2019}
}