Abstract
In this chapter we return to mathematical foundations and discuss the theory of stable distributions as an extension to the central limit theorem and the canonical representation of stable distributions. The solution of the one-dimensional Weierstrass random walk is presented in detail, including its fractal properties and super-diffusive behavior. Fractal time random walks and their relation to subdiffusive behavior are introduced next. Finally, we discuss the truncated Levy flight which will be employed in Chap. 5 for the description of financial fluctuations.
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