The law of the iterated logarithm for algorithmically random Brownian motion

被引：9

作者：

Kjos-Hanssen, Bjorn ^{[1
]}

Nerode, Anil ^{[1
]}

机构：

[1] Cornell Univ, Dept Math, White Hall, Ithaca, NY 14853 USA

来源：

LOGICAL FOUNDATIONS OF COMPUTER SCIENCE, PROCEEDINGS | 2007年 / 4514卷

关键词：

Brownian motion; randomness; law of the iterated logarithm; Kolmogorov complexity;

D O I：

10.1007/978-3-540-72734-7_22

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Algorithmic randomness is most often studied in the setting of the fair-coin measure on the Cantor space, or equivalently Lebesgue measure on the unit interval. It has also been considered for the Wiener measure on the space of continuous functions. Answering a question of Fouche, we show that Khintchine's law of the iterated logarithm holds at almost all points for each Martin-Lof random path of Brownian motion. In the terminology of Fouche, these are the complex oscillations. The main new idea of the proof is to take advantage of the Wiener-Caratheodory measure algebra isomorphism theorem.

引用

页码：310 / +

页数：3