The area of a spectrally positive stable process stopped at zero

  1. Julien Letemplier
  2. Thomas Simon

Abstract

 

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.

 

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Probability and Mathematical Statistics

38, z. 1, 2018

Pages from 27 to 37

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