Occupancy Schemes Associated to Yule Processes - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2008

Occupancy Schemes Associated to Yule Processes

Florian Simatos
  • Function : Author
  • PersonId : 841874


An occupancy problem with an infinite number of bins and a random probability vector for the locations of the balls is considered. The respective sizes of bins are related to the split times of a Yule process. The asymptotic behavior of the landscape of first empty bins, i.e., the set of corresponding indices represented by point processes, is analyzed and convergences in distribution to mixed Poisson processes are established. Additionally, the influence of the random environment, the random probability vector, is analyzed. It is represented by two main components: an i.i.d.\ sequence and a fixed random variable. Each of these components has a specific impact on the qualitative behavior of the stochastic model. It is shown in particular that for some values of the parameters, some rare events, which are identified, play an important role on average values of the number of empty bins in some regions.
Fichier principal
Vignette du fichier
Hal.pdf (267.49 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

inria-00331511 , version 1 (17-10-2008)


  • HAL Id : inria-00331511 , version 1
  • ARXIV : 0810.3079


Philippe Robert, Florian Simatos. Occupancy Schemes Associated to Yule Processes. 2008. ⟨inria-00331511⟩


65 View
150 Download



Gmail Facebook X LinkedIn More