2013/03/04 by Paul Potgieter, Potgieter, Paul
Economics, Econometrics and Finance · Mathematics · #28A80 #42B10 #43A46 #60G17 #60J65 #Complex Systems and Time Series Analysis #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications
paper · doi:10.48550/arxiv.1303.0678
openalex publication_date 2013/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Robert Kaufman's proof that the set of rapid points of Brownian motion has a Fourier dimension equal to its Hausdorff dimension was first published in 1974. A study of the proof of the original paper revealed several gaps in the arguments and a slight inaccuracy in the main theorem. This paper presents a new version of the construction and incorporates some recent results in order to establish a corrected version of Kaufman's theorem. The method of proof can then be extended to show that functionally determined rapid points of Brownian motion also form Salem sets for absolutely continuous functions of finite energy.