arXiv Analytics

Sign in

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.

Related articles:
arXiv:1611.07551 [math.PR] (Published 2016-11-22)
Maximal irreducibility measure for spatial birth-and-death processes
arXiv:1101.4765 [math.PR] (Published 2011-01-25, updated 2011-06-15)
Binary jumps in continuum. I. Equilibrium processes and their scaling limits