{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:39:39Z","timestamp":1753889979788,"version":"3.41.2"},"reference-count":13,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2012,3,9]],"date-time":"2012-03-09T00:00:00Z","timestamp":1331251200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>By considering a counting-type argument on Brownian sample paths, we prove a\nresult similar to that of Orey and Taylor on the exact Hausdorff dimension of\nthe rapid points of Brownian motion. Because of the nature of the proof we can\nthen apply the concepts to so-called complex oscillations (or 'algorithmically\nrandom Brownian motion'), showing that their rapid points have the same\ndimension.<\/jats:p>","DOI":"10.2168\/lmcs-8(1:23)2012","type":"journal-article","created":{"date-parts":[[2012,9,6]],"date-time":"2012-09-06T10:03:11Z","timestamp":1346925791000},"source":"Crossref","is-referenced-by-count":0,"title":["The rapid points of a complex oscillation"],"prefix":"10.46298","volume":"Volume 8, Issue 1","author":[{"given":"Paul","family":"Potgieter","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2012,3,9]]},"reference":[{"key":"10.2168\/LMCS-8(1:23)2012_Asarin","first-page":"21","volume":"47","author":"Asarin, E.A. and Pokrovskii, A.V.","year":"1986","journal-title":"Automation and Remote Control"},{"key":"10.2168\/LMCS-8(1:23)2012_Cutland","unstructured":"Cutland, N.J.Loeb Measures in Practice: Recent Advances. 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