Vectorial multifractal measures theories and applications to branching random walks Najmeddine Attia, Amal Mahjoub

Format:

Book

Author/Creator:

Attia, Najmeddine, author.

Mahjoub, Amal, author.

Series:

SpringerBriefs in mathematics 2191-8201

SpringerBriefs in Mathematics 2191-8201

Language:

English

Subjects (All):

Multifractals.

Fractal analysis.

Random walks (Mathematics).

Physical Description:

1 online resource

illustration

Edition:

1st ed.

Place of Publication:

Cham Springer 2026

Summary:

This book introduces a new multifractal vectorial formalism based on Hewitt-Stromberg measures, with particular emphasis on its application to branching random walks on the Galton-Watson tree. This formalism relies on the use of vector-valued functions defined on balls in a metric space and taking values in a Banach space, thus offering a generalization of classical multifractal analysis. These measures lie between Hausdorff and packing measures and then, the authors' study is specially imported especially when the classical multifractal formalism does not hold. The authors investigate the fractal dimension of the sets of infinite branches of the boundary of a super-critical Galton-Watson tree (endowed with a random metric) along which the averages of a valued branching random walk, have a given set of limit points. Furthermore, the authors examine additional general sets of levels in multifractal analysis, leading to the development of a relative multifractal vectorial formalism. They explore this relative formalism within the framework of the branching random walk

Contents:

Introduction

Vectorial multifractal measures and dimensions

A relative vectorial multifractal formalism of the level sets X (alpha)

A relative vectorial multifractal formalism of the level sets X (alpha, beta)

Relative multifractal formalism of branching random walk with random metric

Appendix

Notes:

Includes bibliographical references

Online resource; title from PDF title page (SpringerLink, viewed May 4, 2026)

Other Format:

Print version Attia, Najmeddine Vectorial Multifractal Measures

ISBN:

9783032200655

3032200652

OCLC:

1588214064

Access Restriction:

Restricted for use by site license