Abstract
Stable distributions are special types of probability distributions whose origin is a particular limit regime of other types of distributions. They are closely related to the simple convolution process, which is introduced first for continuous and then for discrete random variables. This leads to the central limit theorem as one of the most important results of probability theory, as well as to its generalized version which is useful in the analysis of random walks. Extreme-value distributions are also presented, as they possess a limit theorem of their own (Fisher–Tippett–Gnedenko). The last part is devoted to the discussion of discrete-time and continuous-time random walks, together with their characteristic diffusion properties.
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Širca, S. (2016). Stable Distributions and Random Walks. In: Probability for Physicists. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-31611-6_6
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