A hard-core stochastic process with simultaneous births and deaths. Issue 4 (2nd October 2018)

• Record Type: Journal Article
• Authors: Manjrekar, Mayank
• Is Part Of: Stochastic models. Volume 34:Issue 4(2018)
• Page Start: 375
• Page End: 396
• Publication Date: 2018-10-02
• Subjects: Random sequential adsorption -- point processes -- spatial birth-death processes -- hard-core point process -- coupling from the past; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/15326349.2018.1505529
• Languages: English
• ISSNs: 1532-6349

Abstract

Abstract: We introduce and examine a class of stochastic spatial point processes with births and deaths, related to spatial loss networks introduced in Ferrari et al. In these processes, a point stays in the system until it is removed due to interaction with a conflicting new arrival. In particular, we consider an interaction scheme where two points are conflicting if closed balls of radius 1/2 around them overlap and a new arriving point " kills" each conflicting point independently with probability ρ . The new point is accepted if all conflicting points are killed. We construct this process on the whole Euclidean space R d, d ∈ N + . If ρ is large enough, we show existence of a stationary regime and exponential convergence to the stationary distribution. Such stochastic models have been studied earlier as models for populations of interacting individuals or as spatial queuing and resource sharing networks.