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Non-homogenous bivariate fragmentation process: asymptotic distribution via contraction method
  • Rafik Aguech,
  • Samia Ilji
Rafik Aguech
KSU
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Samia Ilji
University of Monastir
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Abstract

In this paper we investigate the size of a bi-dimensional fragmentation process. A rectangle of dimensions x and y is considered, it is split into four sub-rectangles with some probability that depends on x and y, we iterate until the stop of the process. The total number of the all the obtained rectangles at the end of the process satisfies some equality in distribution which is resolved , using some tools on integral equations, via the contraction method.

Peer review status:ACCEPTED

11 Feb 2020Submitted to Mathematical Methods in the Applied Sciences
21 Feb 2020Submission Checks Completed
21 Feb 2020Assigned to Editor
13 Jul 2020Reviewer(s) Assigned
18 Nov 2020Review(s) Completed, Editorial Evaluation Pending
19 Nov 2020Editorial Decision: Revise Minor
09 Dec 20201st Revision Received
09 Dec 2020Submission Checks Completed
09 Dec 2020Assigned to Editor
09 Dec 2020Editorial Decision: Accept