On the rate of convergence for Takagi class functions

被引：0

作者：

Osaka, Shoto ^{[1
]}

Takei, Masato ^{[2
]}

机构：

[1] Yokohama Natl Univ, Grad Sch Engn Sci, Yokohama, Kanagawa, Japan

[2] Yokohama Natl Univ, Fac Engn, Dept Appl Math, Yokohama, Kanagawa, Japan

来源：

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS | 2020年 / 37卷 / 01期

关键词：

Nowhere differentiable continuous functions; Probabilistic method; Limit theorems; Martingales; ITERATED LOGARITHM;

D O I：

10.1007/s13160-019-00398-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a generalized version of the Takagi function, which is one of the most famous example of nowhere differentiable continuous functions. We investigate a set of conditions to describe the rate of convergence of Takagi class functions from the probabilistic point of view: The law of large numbers, the central limit theorem, and the law of the iterated logarithm. On the other hand, we show that the Takagi function itself does not satisfy the law of large numbers in the usual sense.

引用

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页码：193 / 212

页数：20

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