A Grain of Dust Falling Through a Sierpinski Gasket

作     者：Samantha LEORATO Enzo ORSINGHER 

作者机构：Dipartimento di StatisticaProbabilitd e Statistiche ApplicateUniversity of Rome "La Sapienza"P.le A.Moro5-00185 RomaItaly 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2007年第23卷第6期

页      面：1095-1108页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：We gratefully acknowledge the support of the NATO grant PST.CLG.980408 The research is also supported by a grant from MIUR,Italy 

主　　题：Binomial random variables fractals Hausdorff dimension random walks self-similarity 

摘      要：In this paper we analyze the downward random motion of a particle in a vertical, bounded, Sierpinski gasket G, where at each layer either absorption or delays are considered. In the case of motion with absorption the explicit distribution of the position of the descending particle in the pre-gasket Gn is obtained and the limiting case of the Sierpinski gasket discussed. For the delayed downward motion we derive a representation of the random time needed to arrive at the base of Gn in terms of independent binomial random variables （containing the contribution of delays at different layers with different geometrical structures）.