LEVY, Calcul des probabilités, 1925
LEVY, Paul.
Calcul des probabilités.
Paris, Gauthier-Villars, 1925.
8vo (255x166 mm), viii-350-(1) pages. binding : Original printed wrappers.
First edition.
Paul Lévy (1886-1971) French mathematician is among the founders of modern probability theory. We also owe him important considerations on the stable stochastic laws which bear his name as well as on martingales. In 1920, he was appointed professor of analysis at the École Polytechnique and on this occasion discovered the discipline that would leave his mark the most: the calculation of probabilities. It can be said that most of the essential concepts of probability theory derive from him.
references: Mandelbrot [The variation of certain speculative prices in. The journal of Business. 1963 : "I shall replace the Gaussian distributions throughout by another family of probability laws, to be referred to as 'stable Paretian,' which were first described in Paul Levy's classic 'Calcul des probabilités' (1925)"], Loève [Paul LEVY, 1886-1971 in The Annals of probablility. 1973 : "Paul Levy's study of stable laws led him to a completely novel approach to the problem of limits laws which for two centuries was the central and, in fact, the only theoretical problem of Calculus of Probabilities. From Bernoulli (1713) and de Moivre (1732) to Liapounov (1900) and Lindeberg (1920), it consisted of the search of conditions for the limits laws of sequences of normed sums of independant random variables with finite second moments to be Gaussian or degenerate.
Paul Lévy in his 1925 book transforms the old central limit problem into the search all possible limit laws for sequences of suitably normed sums of independent (and identically distributed) random variables, not necessary having finite second moments and then for necessary and sufficient conditions for convergence to any given stable law Poisson's limiting procedure and his limit law stood isolated and ignored until 1934"].
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