The area of a spectrally positive stable process stopped at zero
A multiplicative identity in law for the area of a spectrally positive Lévy ∝-stable process stopped at zero is established. Extending that of Lefebvre for Brownian motion, it involves an inverse beta random variable and the square of a positive stable random variable. This simple identity makes it possible to study precisely the behaviour of the density at zero, which is Fréchet-like.
2018 ◽
Vol 21
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1980 ◽
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pp. 301-312
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