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Contents of PMS, Vol. 38, Fasc. 1,
pages 27 - 37
 

THE AREA OF A SPECTRALLY POSITIVE STABLE PROCESS STOPPED AT ZERO

Julien Letemplier
Thomas Simon

Abstract: A multiplicative identity in law for the area of a spectrally positive Lévy α -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.

2010 AMS Mathematics Subject Classification: Primary: 60G52; Secondary: 60E07, 60G51.

Keywords and phrases: Hitting time, integrated process, stable Lévy process, tail asymptotics.

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