Fractal Poisson processes

被引：8
作者：
Eliazar, Iddo [1 ]
Klafter, Joseph [2 ]
机构：
[1] Holon Inst Technol, Dept Technol Management, IL-58102 Holon, Israel
[2] Tel Aviv Univ, Sackler Fac Exact Sci, Sch Chem, IL-69978 Tel Aviv, Israel
来源：
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2008年 / 387卷 / 21期
关键词：
fractal Poisson processes; stochastic limit-laws; nonlinear scaling; power-laws; self-similarity; Central Limit Theorem (CLT); Extreme Value Theory (EVT);
D O I：
10.1016/j.physa.2008.05.011
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
The Central Limit Theorem (CLT) and Extreme Value Theory (EVT) study, respectively, the stochastic limit-laws of sums and maxima of sequences of independent and identically distributed (i.i.d.) random variables via an affine scaling scheme. In this research we study the stochastic limit-laws of populations of i.i.d. random variables via nonlinear scaling schemes. The stochastic population-limits obtained are fractal Poisson processes which are statistically self-similar with respect to the scaling scheme applied, and which are characterized by two elemental structures: (i) a universal power-law structure common to all limits, and independent of the scaling scheme applied; (ii) a specific structure contingent on the scaling scheme applied. The sum-projection and the maximum-projection of the population-limits obtained are generalizations of the classic CLT and EVT results extending them from affine to general nonlinear scaling schemes. (C) 2008 Elsevier B.V. All rights reserved.
引用
收藏
页码：4985 / 4996
页数：12
相关论文
共 20 条
  • [11] Ibragimov I. A., 1971, Independent and Stationary Sequences of Random Variables
  • [12] Janicki A, 1994, SIMULATION CHAOTIC B
  • [13] Kingman J. F. C., 1993, POISSON PROCESSES
  • [14] Kotz S., 2000, Extreme Value Distributions: Theory and Applications
  • [15] Levy P, 1954, THEORIE ADDITION VAR, VSecond
  • [16] Meerschaert M.M., 2001, WILEY PROB STAT
  • [17] Rachev S, 2000, STABLE PARETIAN MODE
  • [18] RESNICK S, 2005, 2005024 EUR
  • [19] RESNICK S, 2006, HEAVY TAILED PHENOME
  • [20] Samorodnitsky G., 1994, STABLE NONGAUSSIAN R
12