The theory of stable probability distributions and their domains of attraction is derived in a direct way (avoiding the usual route via infinitely divisible distributions) using Fourier transforms. Regularly varying functions play an important role in the exposition.

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Tinbergen Institute Discussion Paper Series
Tinbergen Institute

Geluk, J.L, & de Haan, L.F.M. (1997). Stable Probability Distributions and their Domains of Attraction (No. TI 97-089/4). Tinbergen Institute Discussion Paper Series. Retrieved from