Algorithmically random series and Brownian motion

被引：1

作者：

Potgieter, Paul ^{[1
]}

机构：

[1] Univ South Africa, Dept Decis Sci, POB 392, ZA-0003 Pretoria, South Africa

来源：

ANNALS OF PURE AND APPLIED LOGIC | 2018年 / 169卷 / 11期

关键词：

Martin-Lof randomness; Rademacher series; Fourier series; Brownian motion; COMPLEXITY;

D O I：

10.1016/j.apal.2018.07.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider some random series parametrised by Martin-Lof random sequences. The simplest case is that of Rademacher series, independent of a time parameter. This is then extended to the case of Fourier series on the circle with Rademacher coefficients. Finally, a specific Fourier series which has coefficients determined by a computable function is shown to converge to an algorithmically random Brownian motion. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：1210 / 1226

页数：17

共 20 条

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