MULTIFRACTAL ANALYSIS OF ONE-DIMENSIONAL BIASED WALKS-Reference-Cited by-同舟云学术

MULTIFRACTAL ANALYSIS OF ONE-DIMENSIONAL BIASED WALKS

Published:2018-06 Issue:03 Volume:26 Page:1850030
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

CHEN YUFEI¹,DAI MEIFENG¹^ORCID,WANG XIAOQIAN¹,SUN YU¹,SU WEIYI²

Affiliation:

1. Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang 212013, P. R. China

2. Department of Mathematics, Nanjiang University, Nanjing 210093, P. R. China

Abstract

For an infinite sequence [Formula: see text] of [Formula: see text] and [Formula: see text] with probability [Formula: see text] and [Formula: see text], we mainly study the multifractal analysis of one-dimensional biased walks. Let [Formula: see text] and [Formula: see text]. The Hausdorff and packing dimensions of the sets [Formula: see text] are [Formula: see text], which is the development of the theorem of Besicovitch [On the sum of digits of real numbers represented in the dyadic system, Math. Ann. 110 (1934) 321–330] on random walk, saying that: For any [Formula: see text], the set [Formula: see text] has Hausdorff dimension [Formula: see text].

Funder

National Natural Science Foundation of China

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Geometry and Topology,Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X18500305

Reference8 articles.

1. On the sum of digits of real numbers represented in the dyadic system.

2. HAUSDORFF MEASURE OF CARTESIAN PRODUCT OF THE TERNARY CANTOR SET

3. Two types of weight-dependent walks with a trap in weighted scale-free treelike networks

4. A multifractal decomposition according to rate of returns

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