Approximation and Wasserstein distance for self-similar measures on the unit interval

被引：3

作者：

Lichtenegger, Emily ^{[1
]}

Niedzialomski, Robert ^{[2
]}

机构：

[1] Univ Missouri, Dept Math, 202 Math Sci Bldg,810 East Rollins St, Columbia, MO 65211 USA

[2] Univ Tennessee Martin, Dept Math & Stat, 424 Humanities Bldg, Martin, TN 38238 USA

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 474卷 / 02期

关键词：

Self-similar measure; Hutchinson operator; Wasserstein distance; COUPLINGS;

D O I：

10.1016/j.jmaa.2019.02.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the Wasserstein distance between self-similar measures associated to two non-overlapping linear contractions of the unit interval. The main theorem gives an explicit formula for the Wasserstein distance between iterations of certain discrete approximations of such measures. Our argument extends to two non-overlapping contractions with different contraction ratios and our result allows us to recover the formula for the Wasserstein distance between self-similar measures previously obtained. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：1250 / 1266

页数：17

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