Stochastic Equation of Fragmentation and Branching Processes Related to Avalanches

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• 作者：Lucian Beznea ; Madalina Deaconu ; Oana Lupaşcu
• 关键词：Fragmentation kernel ; Avalanche ; Branching process ; Stochastic differential equation of fragmentation ; Space of fragmentation sizes ; 60J80 ; 60J45 ; 60J35 ; 60K35
• 刊名：Journal of Statistical Physics
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：162
• 期：4
• 页码：824-841
• 全文大小：530 KB
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• 作者单位：Lucian Beznea (1) (2)
  Madalina Deaconu (3) (4)
  Oana Lupaşcu (3) (4) (5) (6)
  
  1. Simion Stoilow Institute of Mathematics of the Romanian Academy, Research Unit No. 2, P.O. Box 1-764, 014700, Bucharest, Romania
  2. Faculty of Mathematics and Computer Science, University of Bucharest, Bucharest, Romania
  3. Inria, 54600, Villers-lès-Nancy, France
  4. Université de Lorraine, CNRS, Institut Elie Cartan de Lorraine - UMR 7502, 54506, Vandoeuvre-lès-Nancy, France
  5. Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, Calea 13 Septembrie 13, Bucharest, Romania
  6. The Research Institute of the University of Bucharest (ICUB), Bucharest, Romania
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Statistical Physics
  Mathematical and Computational Physics
  Physical Chemistry
  Quantum Physics
  
• 出版者：Springer Netherlands
• ISSN：1572-9613

文摘

We give a stochastic model for the fragmentation phase of an avalanche. We construct a fragmentation-branching process related to the avalanches, on the set of all fragmentation sizes introduced by Bertoin. A fractal property of this process is emphasized. We also establish a specific stochastic differential equation of fragmentation. It turns out that specific branching Markov processes on finite configurations of particles with sizes bigger than a strictly positive threshold are convenient for describing the continuous time evolution of the number of the resulting fragments. The results are obtained by combining analytic and probabilistic potential theoretical tools. Keywords Fragmentation kernel Avalanche Branching process Stochastic differential equation of fragmentation Space of fragmentation sizes