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Nonhomogenous bivariate fragmentation process: Asymptotic distribution via contraction method
Author(s) -
Aguech Rafik,
Ilji Samia
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7186
Subject(s) - mathematics , bivariate analysis , contraction (grammar) , fragmentation (computing) , rectangle , mathematical analysis , geometry , statistics , computer science , medicine , operating system
In this paper, we investigate the size of a bidimensional fragmentation process. A rectangle of dimensions x and y is considered; it is split into four subrectangles 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 by the contraction method and by some tools on integral equations.