Self-similar Fragmentations
نویسنده
چکیده
We introduce a probabilistic model that is meant to describe an object that falls apart randomly as time passes and fulfills a certain scaling property. We show that the distribution of such a process is determined by its index of self-similarity , a rate of erosion c�0, and a so-called Lévy measure that accounts for sudden dislocations. The key of the analysis is provided by a transformation of self-similar fragmentations which enables us to reduce the study to the homogeneous case �=0 which is treated in [6]. DOI: https://doi.org/10.1016/S0246-0203(00)01073-6 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-79461 Published Version Originally published at: Bertoin, Jean (2002). Self-similar fragmentations. Annales de l’Institut Henri Poincaré (B) Probabilities et Statistiques, 38(3):319-340. DOI: https://doi.org/10.1016/S0246-0203(00)01073-6 Ann. I. H. Poincaré – PR 38, 3 (2002) 319–340 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved S0246-0203(00)01073-6/FLA SELF-SIMILAR FRAGMENTATIONS
منابع مشابه
Regularity of formation of dust in self-similar fragmentations
In self-similar fragmentations with a negative index, fragments split even faster as their mass is smaller, so that the fragmentation runs away and some mass is reduced to dust. Our purpose is to investigate the regularity of this formation of dust. Let M(t) denote the mass of dust at time t.We give some sufficient and some necessary conditions for the measure dM to be absolutely continuous. In...
متن کاملAsymptotics for the small fragments of the fragmentation at nodes
Abstract. We consider the fragmentation at nodes of the Lévy continuous random tree introduced in a previous paper. In this framework we compute the asymptotic for the number of small fragments at time θ. This limit is increasing in θ and discontinuous. In the α-stable case the fragmentation is self-similar with index 1/α, with α ∈ (1, 2) and the results are close to those Bertoin obtained for ...
متن کاملAsymptotic laws for nonconservative self-similar fragmentations
We consider a self-similar fragmentation process in which the generic particle of mass x is replaced by the offspring particles at probability rate x, with positive parameter α. The total of offspring masses may be both larger or smaller than x with positive probability. We show that under certain conditions the typical mass in the ensemble is of the order t and that the empirical distribution ...
متن کاملStrong Convergence of Partial Match Queries in Random Quadtrees
We prove that the rescaled costs of partial match queries in a random two-dimensional quadtree converge almost surely towards a random limit which is identified as the terminal value of a martingale. Our approach shares many similarities with the theory of self-similar fragmentations.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000