Algorithmically random series and Brownian motion |
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Authors: | Paul Potgieter |
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Affiliation: | Department of Decision Sciences, University of South Africa, P.O. Box 392, Pretoria 0003, South Africa |
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Abstract: | We consider some random series parametrised by Martin-Löf random sequences. The simplest case is that of Rademacher series, independent of a time parameter. This is then extended to the case of Fourier series on the circle with Rademacher coefficients. Finally, a specific Fourier series which has coefficients determined by a computable function is shown to converge to an algorithmically random Brownian motion. |
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Keywords: | 68Q30 42A20 42A38 60G15 Martin-Löf randomness Rademacher series Fourier series Brownian motion |
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