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A direct approach to the stable distributions

  • E. J. G. Pitman and Jim Pitman (a1)

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.

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Corresponding author

Statistics Department, University of California, Berkeley, 367 Evans Hall, Berkeley, CA94720‒3860, USA. Email address: pitman@stat.berkeley.edu

References

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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
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