Abstract
We introduce a class of quasi-stable stochastic process, the truncated Lévy Flight (TLF). A TLF is a stochastic process with finite variance. We show theoretically and numerically that the convergence of the sum of n independent TLF to a. Gaussian process is usually extremely slow. In fact a remarkably large value of n can be required to ensure the convergence to a Gaussian process. We also investigate the statistical properties of the S&P 500 (a financial index) and we show that they are qualitatively in agreement with the one of a TLF.
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References
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© 1995 Springer-Verlag
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Mantegnal, R.N., Stanley, H.E. (1995). Ultra-slow convergence to a Gaussian: The truncated Lévy flight. In: Shlesinger, M.F., Zaslavsky, G.M., Frisch, U. (eds) Lévy Flights and Related Topics in Physics. Lecture Notes in Physics, vol 450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59222-9_42
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DOI: https://doi.org/10.1007/3-540-59222-9_42
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