Fractional Brownian motion approximation based on fractional integration of a white noise |
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| Institution: | 1. National Science Center, Kharkov Institute of Physics and Technology, Institute for Theoretical Physics, Akademicheskaya st.1, 310108 Kharkov, Ukraine;2. Institute for Single Crystals, National Academy of Sciences of Ukraine, Lenin ave. 60, 310001 Kharkov, Ukraine;1. Department of Mathematics, Bannari Amman Institute of Technology, Sathyamangalam, Erode 638401, Tamilnadu, India;2. Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Kalavakkam-603110, Chengalpattu, Tamilnadu, India;1. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Building 27, 1 Gwanak-ro, Gwanak-gu, Seoul 151-747, Republic of Korea;2. Department of Mathematics, University of Illinois, Urbana, IL 61801, USA;3. Department of Mathematics, University of Zagreb, Zagreb, Croatia |
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| Abstract: | We study simple approximations to fractional Gaussian noise and fractional Brownian motion. The approximations are based on spectral properties of the noise. They allow one to consider the noise as the result of fractional integration/differentiation of a white Gaussian noise. We consider correlation properties of the approximation to fractional Gaussian noise and point to the peculiarities of persistent and anti-persistent behaviors. We also investigate self-similarity properties of the approximation to fractional Brownian motion, namely, `τH laws' for the structure function and the range. We conclude that the models proposed serve as a convenient tool for modelling of natural processes and testing and improvement of methods aimed at analysis and interpretation of experimental data. |
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