A direct approach to the stable distributions. (July 2016)

• Record Type: Journal Article
• Authors: Pitman, E. J. G.; Pitman, Jim
• Editors: Goldie, C. M.; Mijatović, A.
• Is Part Of: Advances in applied probability. Volume 48:Number A(2016)
• Page Start: 261
• Page End: 282
• Publication Date: 2016-07
• Subjects: Stable distribution, -- characteristic function, -- regular variation, -- infinitely divisible distribution, -- Lévy‒Khintchine formula, -- Eulerian integral; Primary 60E07; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2016.55
• Languages: English
• ISSNs: 0001-8678

Abstract

Abstract: The explicit form for the characteristic function of a stable distribution on the line is derived analytically by solving the associated functional equation and applying the theory of regular variation, without appeal to the general Lévy‒Khintchine integral representation of infinitely divisible distributions.