Algorithmic information theory
Algorithmic information theory
Dynamics of a generic Brownian motion: Recursive aspects
Theoretical Computer Science
The Law of the Iterated Logarithm for Algorithmically Random Brownian Motion
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
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A continuous function x on the unit interval is an algorithmically random Brownian motion when every probabilistic event A which holds almost surely with respect to the Wiener measure, is reflected in x , provided A has a suitably effective description. In this paper we study the zero sets and global maxima from the left as well as the images of compact sets of reals of Hausdorff dimension zero under such a Brownian motion. In this way we shall be able to find arithmetical definitions of perfect sets of reals whose elements are linearly independent over the field of recursive real numbers.