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A direct approach to the stable distributions
Part of
- Distribution theory - Probability
E. J. G. Pitman, Jim Pitman
Journal:

Advances in Applied Probability / Volume 48 / Issue A / July 2016

Published online by Cambridge University Press:

25 July 2016, pp. 261-282

Print publication:

July 2016
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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.

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A direct approach to the stable distributions