ABSTRACT
The term stable was coined by Paul Lévy. Lévy gives not only the characteristic functions of all SaS laws but also those of all strictly stable laws. Many textbooks contain an introduction to stable laws. Lukács devotes a number of sections to the analytic properties of stable distributions. The classic introductions to stable laws have been for many years Gnedenko and Kolmogorov and Feller. An encylopedic treatment of stable laws on the real line is given by Zolotarev, a work later translated into English. A series representation of infinitely divisible random variables without a Gaussian component was established by Ferguson and Klass and developed by LePage. Analytic properties of stable densities were a major topic of research in the 1930s, 1940s and 1950s. The a-stable distributions are all unimodal. A typical assumption is that the normalized sum of an "independent imitation" converges to a stable law. Linear fractional stable noise is the increment of linear fractional stable motion.
