 The evolution of a spatial stochastic networkPhilippe Robert Stochastic Processes and their Applications, 2010, vol. 120, issue 7, 1342-1363 Abstract: The asymptotic behavior of a stochastic network represented by a birth and death processes of particles on a compact state space is analyzed. In the births, particles are created at rate [lambda]+ and their location is independent of the current configuration. Deaths are due to negative particles arriving at rate [lambda]-. The death of a particle occurs when a negative particle arrives in its neighborhood and kills it. Several killing schemes are considered. The arriving locations of positive and negative particles are assumed to have the same distribution. By using a combination of monotonicity properties and invariance relations it is shown that the configurations of particles converge in distribution for several models. The problems of uniqueness of invariant measures and of the existence of accumulation points for the limiting configurations are also investigated. It is shown for several natural models that if [lambda]+ Keywords: Stochastic; networks; Queueing; systems; Birth; and; death; processes; Stationary; recursive; equations; Random; point; processes; Backward; coupling; Stationary; point; processes (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:120:y:2010:i:7:p:1342-1363 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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