By Philipp Frank, Richard Von Mises
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Professor Kuang-Chao Chou (also often called Guang-Zhao Zhou) is the previous President of chinese language Academy of Sciences. He has been elected because the Academician of chinese language Academy of Sciences, international affiliate of the USA nationwide Academy of Sciences, Fellow of the 3rd international Academy of technology, overseas Member of Soviet (Russian) Academy of Sciences, Czechoslovak Academy of Sciences, Bulgarian Academy of Sciences, Romania Academy of Sciences, Mongolian Academy of Sciences, the eu Academy of Arts, Sciences and arts, Membre fondateur Academie Francophone d'Ingenieurs.
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Extra info for Die Differential und IntegralGleichungen der Mechanik und Physik. volume 1, Second Edition
18. A. W. Lo and A. C. MacKinlay, A Non-Random Walk Down Wall Street. (Princeton University Press, 2001). 19. T. Di Matteo, Multi-scaling in finance, Quantitative Finance. 7, 21–36, (2007). 20. T. Di Matteo, T. Aste, and M. M. Dacorogna, Scaling behaviors in differently developed markets, Physica A. , (2003). 21. T. Di Matteo, T. Aste, and M. M. Dacorogna, Long term memories of developed and emerging markets: using the scaling analysis to characterize their stage of development, Journal of Banking & Finance.
Such a difference is reflected in the diffusion dynamics of the random walker. 1. Super-diffusive processes In additive stochastic processes [such as Eq. e. p(η) ∼ |η|−α−1 , with 0 < α < 2), all the motion is dominated by the large fluctuations and it results in a super-diffusive behavior where the mean January 6, 2010 22 17:1 World Scientific Review Volume - 9in x 6in SS22˙Master T. Aste and T. Di Matteo square displacement increases faster than τ . Let us here give an heuristic simple derivation of this fact which shows clearly the origin of anomalous diffusion behavior in presence of power law noise.
I. M. Langlands and P. 1 Diffusion on fractals . . . . . . . . . . 2 Fractional Brownian motion . . . . . . . . 3 Continuous time random walks and power laws . . 4 Simulating random walks for fractional diffusion . . 5 Fractional Fokker–Planck equations . . . . . . 6 Fractional Reaction-Diffusion equations . . . . . 7 Fractional diffusion based models . . . . . . 8 Power laws and fractional diffusion . . . . . . 3 Appendix: Introduction to fractional calculus .