Multifractal products of cylindrical pulses

被引：146

作者：

Barral, J

Mandelbrot, BB

机构：

[1] Inst Natl Rech Informat & Automat, Project Fractales, F-78153 Le Chesnay, France

[2] Yale Univ, Dept Math, New Haven, CT 06520 USA

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2002年 / 124卷 / 03期

关键词：

random measures; multifractal analysis; continuous time martingales; statistically self-similar; Poisson point processes;

D O I：

10.1007/s004400200220

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

New multiplicative and statistically self-similar measures A are defined on R as limits of measure-valued martingales. Those martingales are constructed by multiplying random functions attached to the points of a statistically self-similar Poisson point process defined in a strip of the plane. Several fundamental problems are solved, including the non-degeneracy and the multiffactal analysis of mu. On a bounded interval, the positive and negative moments of parallel tomuparallel to diverge under broad conditions.

引用

页码：409 / 430

页数：22

共 22 条

[1]

[Anonymous], C R ACAD SCI PARIS A

[2]

Barral J, 1999, PROBAB THEORY REL, V113, P535, DOI 10.1007/s004400050217

[3] Continuity of the multifractal spectrum of a random statistically self-similar measure [J].