The rapid points of a complex oscillation. (English) Zbl 1238.03053
Summary: By considering a counting-type argument on Brownian sample paths, we prove a result similar to that of Orey and Taylor on the exact Hausdorff dimension of the rapid points of Brownian motion. Because of the nature of the proof we can then apply the concepts to so-called complex oscillations (or algorithmically random Brownian motion), showing that their rapid points have the same dimension.
MSC:
03H05 | Nonstandard models in mathematics |
28A78 | Hausdorff and packing measures |
60G15 | Gaussian processes |
68Q30 | Algorithmic information theory (Kolmogorov complexity, etc.) |