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Anton Muratov (Institutionen för matematiska vetenskaper, matematisk statistik) ; Sergei Zuyev (Institutionen för matematiska vetenskaper, matematisk statistik)
Stochastic Models (1532-6349). Vol. 29 (2013), 4, p. 475-496.
[Artikel, refereegranskad vetenskaplig]

We study a class of dynamically constructed point processes in which at every step a new point (particle) is added to the current configuration with a distribution depending on the local structure around a uniformly chosen particle. This class covers, in particular, generalized Polya urn scheme, Dubins-Freedman random measures, and cooperative sequential adsorption models studied previously. Specifically, we address models where the distribution of a newly added particle is determined by the distance to the closest particle from the chosen one. We address boundedness of the processes and convergence properties of the corresponding sample measure. We show that, in general, the limiting measure is random when it exists and that this is the case for a wide class of almost surely bounded processes.

Denna post skapades 2013-11-29.
CPL Pubid: 187853


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Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)



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Stochastic systems with locally defined dynamics