57 citations · 229 across the 42 of their papers we have counts for
5 papers · 2 filters
A proof of Bondesson's conjecture on stable densities
Pierre Bosch, Thomas Simon
We show that positive -stable densities are hyperbolically completely monotone if and only if . This gives a positive answer to a question raised by L. Bondesson in 19…
The area of a spectrally positive stable process stopped at zero
Julien Letemplier, Thomas Simon
An 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…
Windings of the stable Kolmogorov process
Christophe Profeta, Thomas Simon
We investigate the windings around the origin of the two-dimensional Markov process (X,L) having the stable Lévy process L and its primitive X as coordinates, in the non-trivial ca…
On the infinite divisibility of inverse Beta distributions
Pierre Bosch, Thomas Simon
We show that all negative powers B_{a,b}^-{s} of the Beta distribution are infinitely divisible. The case b<1 follows by complete monotonicity, the case b > 1, s > 1 by hyperbolica…
Persistence of integrated stable processes
Christophe Profeta, Thomas Simon
We compute the persistence exponent of the integral of a stable Lévy process in terms of its self-similarity and positivity parameters. This solves a problem raised by Z. Shi (2003…